LMFDB - Embedded newform 42.8.e.d.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,8,Mod(25,42)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("42.25");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	42.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.1201710703$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 22015x^{4} - 28740x^{3} + 484660225x^{2} - 316355550x + 206496900 $ x^6 + 22015x^4 - 28740x^3 + 484660225x^2 - 316355550x + 206496900
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$0.326375 - 0.565298i$ of defining polynomial
Character	$\chi$	$=$	42.25
Dual form			42.8.e.d.37.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-154.404 - 267.436i) q^{5} +216.000 q^{6} +(517.075 - 745.773i) q^{7} +512.000 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})$	\(q+(-4.00000 - 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-154.404 - 267.436i) q^{5} +216.000 q^{6} +(517.075 - 745.773i) q^{7} +512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(-1235.23 + 2139.49i) q^{10} +(-3241.58 + 5614.58i) q^{11} +(-864.000 - 1496.49i) q^{12} +993.626 q^{13} +(-7235.16 - 599.309i) q^{14} +8337.82 q^{15} +(-2048.00 - 3547.24i) q^{16} +(-15459.7 + 26777.0i) q^{17} +(-2916.00 + 5050.66i) q^{18} +(7794.64 + 13500.7i) q^{19} +19763.7 q^{20} +(10457.7 + 22158.5i) q^{21} +51865.2 q^{22} +(40551.3 + 70236.9i) q^{23} +(-6912.00 + 11971.9i) q^{24} +(-8618.77 + 14928.1i) q^{25} +(-3974.50 - 6884.04i) q^{26} +19683.0 q^{27} +(24788.5 + 52523.9i) q^{28} -34651.6 q^{29} +(-33351.3 - 57766.1i) q^{30} +(-80255.8 + 139007. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-87522.6 - 151594. i) q^{33} +247356. q^{34} +(-279285. - 23133.9i) q^{35} +46656.0 q^{36} +(5542.31 + 9599.55i) q^{37} +(62357.1 - 108006. i) q^{38} +(-13413.9 + 23233.6i) q^{39} +(-79054.9 - 136927. i) q^{40} -459665. q^{41} +(111688. - 161087. i) q^{42} +455951. q^{43} +(-207461. - 359333. i) q^{44} +(-112561. + 194961. i) q^{45} +(324410. - 561895. i) q^{46} +(-149997. - 259803. i) q^{47} +110592. q^{48} +(-288810. - 771240. i) q^{49} +137900. q^{50} +(-417413. - 722980. i) q^{51} +(-31796.0 + 55072.3i) q^{52} +(-948986. + 1.64369e6i) q^{53} +(-78732.0 - 136368. i) q^{54} +2.00205e6 q^{55} +(264742. - 381836. i) q^{56} -420911. q^{57} +(138606. + 240073. i) q^{58} +(1.48133e6 - 2.56574e6i) q^{59} +(-266810. + 462129. i) q^{60} +(1.19185e6 + 2.06435e6i) q^{61} +1.28409e6 q^{62} +(-659304. - 54612.0i) q^{63} +262144. q^{64} +(-153420. - 265731. i) q^{65} +(-700181. + 1.21275e6i) q^{66} +(-2.26696e6 + 3.92649e6i) q^{67} +(-989423. - 1.71373e6i) q^{68} -2.18977e6 q^{69} +(956862. + 2.02748e6i) q^{70} -4.00697e6 q^{71} +(-186624. - 323242. i) q^{72} +(1.73655e6 - 3.00779e6i) q^{73} +(44338.4 - 76796.4i) q^{74} +(-232707. - 403060. i) q^{75} -997714. q^{76} +(2.51106e6 + 5.32064e6i) q^{77} +214623. q^{78} +(346434. + 600041. i) q^{79} +(-632439. + 1.09542e6i) q^{80} +(-265720. + 460241. i) q^{81} +(1.83866e6 + 3.18465e6i) q^{82} +2.65827e6 q^{83} +(-1.56280e6 - 129451. i) q^{84} +9.54818e6 q^{85} +(-1.82381e6 - 3.15892e6i) q^{86} +(467797. - 810248. i) q^{87} +(-1.65969e6 + 2.87466e6i) q^{88} +(686791. + 1.18956e6i) q^{89} +1.80097e6 q^{90} +(513779. - 741019. i) q^{91} -5.19057e6 q^{92} +(-2.16691e6 - 3.75319e6i) q^{93} +(-1.19998e6 + 2.07842e6i) q^{94} +(2.40705e6 - 4.16913e6i) q^{95} +(-442368. - 766204. i) q^{96} +299539. q^{97} +(-4.18807e6 + 5.08590e6i) q^{98} +4.72622e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 81 q^{3} - 192 q^{4} + 70 q^{5} + 1296 q^{6} - 895 q^{7} + 3072 q^{8} - 2187 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 - 81 * q^3 - 192 * q^4 + 70 * q^5 + 1296 * q^6 - 895 * q^7 + 3072 * q^8 - 2187 * q^9	\( 6 q - 24 q^{2} - 81 q^{3} - 192 q^{4} + 70 q^{5} + 1296 q^{6} - 895 q^{7} + 3072 q^{8} - 2187 q^{9} + 560 q^{10} - 2428 q^{11} - 5184 q^{12} - 3838 q^{13} - 3272 q^{14} - 3780 q^{15} - 12288 q^{16} - 24508 q^{17} - 17496 q^{18} + 1353 q^{19} - 8960 q^{20} + 35208 q^{21} + 38848 q^{22} - 96628 q^{23} - 41472 q^{24} - 135175 q^{25} + 15352 q^{26} + 118098 q^{27} + 83456 q^{28} - 228224 q^{29} + 15120 q^{30} - 221395 q^{31} - 98304 q^{32} - 65556 q^{33} + 392128 q^{34} - 136510 q^{35} + 279936 q^{36} - 249987 q^{37} + 10824 q^{38} + 51813 q^{39} + 35840 q^{40} + 1221852 q^{41} - 193320 q^{42} + 1200486 q^{43} - 155392 q^{44} + 51030 q^{45} - 773024 q^{46} + 123114 q^{47} + 663552 q^{48} - 1718583 q^{49} + 2162800 q^{50} - 661716 q^{51} + 122816 q^{52} - 3004752 q^{53} - 472392 q^{54} + 4492720 q^{55} - 458240 q^{56} - 73062 q^{57} + 912896 q^{58} + 2852938 q^{59} + 120960 q^{60} - 665386 q^{61} + 3542320 q^{62} - 298161 q^{63} + 1572864 q^{64} - 5835930 q^{65} - 524448 q^{66} - 10545857 q^{67} - 1568512 q^{68} + 5217912 q^{69} - 6332240 q^{70} - 2039524 q^{71} - 1119744 q^{72} + 6858031 q^{73} - 1999896 q^{74} - 3649725 q^{75} - 173184 q^{76} + 6356164 q^{77} - 829008 q^{78} - 1723021 q^{79} + 286720 q^{80} - 1594323 q^{81} - 4887408 q^{82} + 5271608 q^{83} - 706752 q^{84} + 1474120 q^{85} - 4801944 q^{86} + 3081024 q^{87} - 1243136 q^{88} + 976224 q^{89} - 816480 q^{90} + 9819005 q^{91} + 12368384 q^{92} - 5977665 q^{93} + 984912 q^{94} - 11136310 q^{95} - 2654208 q^{96} - 16971584 q^{97} + 605952 q^{98} + 3540024 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 81 * q^3 - 192 * q^4 + 70 * q^5 + 1296 * q^6 - 895 * q^7 + 3072 * q^8 - 2187 * q^9 + 560 * q^10 - 2428 * q^11 - 5184 * q^12 - 3838 * q^13 - 3272 * q^14 - 3780 * q^15 - 12288 * q^16 - 24508 * q^17 - 17496 * q^18 + 1353 * q^19 - 8960 * q^20 + 35208 * q^21 + 38848 * q^22 - 96628 * q^23 - 41472 * q^24 - 135175 * q^25 + 15352 * q^26 + 118098 * q^27 + 83456 * q^28 - 228224 * q^29 + 15120 * q^30 - 221395 * q^31 - 98304 * q^32 - 65556 * q^33 + 392128 * q^34 - 136510 * q^35 + 279936 * q^36 - 249987 * q^37 + 10824 * q^38 + 51813 * q^39 + 35840 * q^40 + 1221852 * q^41 - 193320 * q^42 + 1200486 * q^43 - 155392 * q^44 + 51030 * q^45 - 773024 * q^46 + 123114 * q^47 + 663552 * q^48 - 1718583 * q^49 + 2162800 * q^50 - 661716 * q^51 + 122816 * q^52 - 3004752 * q^53 - 472392 * q^54 + 4492720 * q^55 - 458240 * q^56 - 73062 * q^57 + 912896 * q^58 + 2852938 * q^59 + 120960 * q^60 - 665386 * q^61 + 3542320 * q^62 - 298161 * q^63 + 1572864 * q^64 - 5835930 * q^65 - 524448 * q^66 - 10545857 * q^67 - 1568512 * q^68 + 5217912 * q^69 - 6332240 * q^70 - 2039524 * q^71 - 1119744 * q^72 + 6858031 * q^73 - 1999896 * q^74 - 3649725 * q^75 - 173184 * q^76 + 6356164 * q^77 - 829008 * q^78 - 1723021 * q^79 + 286720 * q^80 - 1594323 * q^81 - 4887408 * q^82 + 5271608 * q^83 - 706752 * q^84 + 1474120 * q^85 - 4801944 * q^86 + 3081024 * q^87 - 1243136 * q^88 + 976224 * q^89 - 816480 * q^90 + 9819005 * q^91 + 12368384 * q^92 - 5977665 * q^93 + 984912 * q^94 - 11136310 * q^95 - 2654208 * q^96 - 16971584 * q^97 + 605952 * q^98 + 3540024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−154.404	−	267.436i	−0.552413	−	0.956807i	−0.998100	−	0.0616184i	$-0.980374\pi$
$5$	−154.404	−	267.436i	−0.552413	−	0.956807i	0.445687	−	0.895189i	$-0.352960\pi$
$6$	216.000			0.408248
$7$	517.075	−	745.773i	0.569784	−	0.821795i
$7$	517.075	−	745.773i	0.569784	−	0.821795i
$8$	512.000			0.353553
$9$	−364.500	−	631.333i	−0.166667	−	0.288675i
$10$	−1235.23	+	2139.49i	−0.390615	+	0.676565i
$11$	−3241.58	+	5614.58i	−0.734314	+	1.27187i	0.220709	+	0.975340i	$0.429163\pi$
$11$	−3241.58	+	5614.58i	−0.734314	+	1.27187i	−0.955023	+	0.296530i	$0.904170\pi$
$12$	−864.000	−	1496.49i	−0.144338	−	0.250000i
$13$	993.626			0.125436			0.0627178	−	0.998031i	$-0.480023\pi$
$13$	993.626			0.125436			0.0627178	+	0.998031i	$0.480023\pi$
$14$	−7235.16	−	599.309i	−0.704693	−	0.0583717i
$15$	8337.82			0.637872
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−15459.7	+	26777.0i	−0.763186	+	1.32188i	0.178014	+	0.984028i	$0.443033\pi$
$17$	−15459.7	+	26777.0i	−0.763186	+	1.32188i	−0.941200	+	0.337850i	$0.890301\pi$
$18$	−2916.00	+	5050.66i	−0.117851	+	0.204124i
$19$	7794.64	+	13500.7i	0.260710	+	0.451564i	0.966431	−	0.256927i	$-0.0827099\pi$
$19$	7794.64	+	13500.7i	0.260710	+	0.451564i	−0.705720	+	0.708490i	$0.749377\pi$
$20$	19763.7			0.552413
$21$	10457.7	+	22158.5i	0.246415	+	0.522124i
$22$	51865.2			1.03848
$23$	40551.3	+	70236.9i	0.694956	+	1.20370i	0.970195	+	0.242324i	$0.0779096\pi$
$23$	40551.3	+	70236.9i	0.694956	+	1.20370i	−0.275239	+	0.961376i	$0.588757\pi$
$24$	−6912.00	+	11971.9i	−0.102062	+	0.176777i
$25$	−8618.77	+	14928.1i	−0.110320	+	0.191080i
$26$	−3974.50	−	6884.04i	−0.0443482	−	0.0768134i
$27$	19683.0			0.192450
$28$	24788.5	+	52523.9i	0.213402	+	0.452172i
$29$	−34651.6			−0.263834			−0.131917	−	0.991261i	$-0.542113\pi$
$29$	−34651.6			−0.263834			−0.131917	+	0.991261i	$0.542113\pi$
$30$	−33351.3	−	57766.1i	−0.225522	−	0.390615i
$31$	−80255.8	+	139007.i	−0.483850	+	0.838052i	−0.999828	−	0.0185496i	$-0.994095\pi$
$31$	−80255.8	+	139007.i	−0.483850	+	0.838052i	0.515978	+	0.856602i	$0.327428\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$	−87522.6	−	151594.i	−0.423957	−	0.734314i
$34$	247356.			1.07931
$35$	−279285.	−	23133.9i	−1.10106	−	0.0912034i
$36$	46656.0			0.166667
$37$	5542.31	+	9599.55i	0.0179881	+	0.0311562i	0.874879	−	0.484341i	$-0.160941\pi$
$37$	5542.31	+	9599.55i	0.0179881	+	0.0311562i	−0.856891	+	0.515497i	$0.827607\pi$
$38$	62357.1	−	108006.i	0.184350	−	0.319304i
$39$	−13413.9	+	23233.6i	−0.0362102	+	0.0627178i
$40$	−79054.9	−	136927.i	−0.195307	−	0.338282i
$41$	−459665.			−1.04159			−0.520796	−	0.853681i	$-0.674365\pi$
$41$	−459665.			−1.04159			−0.520796	+	0.853681i	$0.674365\pi$
$42$	111688.	−	161087.i	0.232613	−	0.335496i
$43$	455951.			0.874538			0.437269	−	0.899331i	$-0.355946\pi$
$43$	455951.			0.874538			0.437269	+	0.899331i	$0.355946\pi$
$44$	−207461.	−	359333.i	−0.367157	−	0.635935i
$45$	−112561.	+	194961.i	−0.184138	+	0.318936i
$46$	324410.	−	561895.i	0.491408	−	0.851144i
$47$	−149997.	−	259803.i	−0.210737	−	0.365007i	0.741208	−	0.671275i	$-0.234253\pi$
$47$	−149997.	−	259803.i	−0.210737	−	0.365007i	−0.951945	+	0.306268i	$0.900920\pi$
$48$	110592.			0.144338
$49$	−288810.	−	771240.i	−0.350693	−	0.936491i
$50$	137900.			0.156016
$51$	−417413.	−	722980.i	−0.440626	−	0.763186i
$52$	−31796.0	+	55072.3i	−0.0313589	+	0.0543152i
$53$	−948986.	+	1.64369e6i	−0.875577	+	1.51654i	−0.0194308	+	0.999811i	$0.506185\pi$
$53$	−948986.	+	1.64369e6i	−0.875577	+	1.51654i	−0.856147	+	0.516733i	$0.827148\pi$
$54$	−78732.0	−	136368.i	−0.0680414	−	0.117851i
$55$	2.00205e6			1.62258
$56$	264742.	−	381836.i	0.201449	−	0.290548i
$57$	−420911.			−0.301042
$58$	138606.	+	240073.i	0.0932794	+	0.161565i
$59$	1.48133e6	−	2.56574e6i	0.939011	−	1.62641i	0.171690	−	0.985151i	$-0.445077\pi$
$59$	1.48133e6	−	2.56574e6i	0.939011	−	1.62641i	0.767321	−	0.641264i	$-0.221590\pi$
$60$	−266810.	+	462129.i	−0.159468	+	0.276206i
$61$	1.19185e6	+	2.06435e6i	0.672309	+	1.16447i	0.977248	+	0.212101i	$0.0680306\pi$
$61$	1.19185e6	+	2.06435e6i	0.672309	+	1.16447i	−0.304939	+	0.952372i	$0.598636\pi$
$62$	1.28409e6			0.684267
$63$	−659304.	−	54612.0i	−0.332196	−	0.0275167i
$64$	262144.			0.125000
$65$	−153420.	−	265731.i	−0.0692923	−	0.120018i
$66$	−700181.	+	1.21275e6i	−0.299783	+	0.519239i
$67$	−2.26696e6	+	3.92649e6i	−0.920835	+	1.59493i	−0.122708	+	0.992443i	$0.539158\pi$
$67$	−2.26696e6	+	3.92649e6i	−0.920835	+	1.59493i	−0.798127	+	0.602489i	$0.794176\pi$
$68$	−989423.	−	1.71373e6i	−0.381593	−	0.660939i
$69$	−2.18977e6			−0.802466
$70$	956862.	+	2.02748e6i	0.333431	+	0.706501i
$71$	−4.00697e6			−1.32866			−0.664328	−	0.747441i	$-0.731282\pi$
$71$	−4.00697e6			−1.32866			−0.664328	+	0.747441i	$0.731282\pi$
$72$	−186624.	−	323242.i	−0.0589256	−	0.102062i
$73$	1.73655e6	−	3.00779e6i	0.522465	−	0.904936i	−0.477193	−	0.878798i	$-0.658346\pi$
$73$	1.73655e6	−	3.00779e6i	0.522465	−	0.904936i	0.999658	−	0.0261377i	$-0.00832083\pi$
$74$	44338.4	−	76796.4i	0.0127195	−	0.0220308i
$75$	−232707.	−	403060.i	−0.0636934	−	0.110320i
$76$	−997714.			−0.260710
$77$	2.51106e6	+	5.32064e6i	0.626815	+	1.32815i
$78$	214623.			0.0512089
$79$	346434.	+	600041.i	0.0790543	+	0.136926i	0.902842	−	0.429972i	$-0.141477\pi$
$79$	346434.	+	600041.i	0.0790543	+	0.136926i	−0.823788	+	0.566898i	$0.808143\pi$
$80$	−632439.	+	1.09542e6i	−0.138103	+	0.239202i
$81$	−265720.	+	460241.i	−0.0555556	+	0.0962250i
$82$	1.83866e6	+	3.18465e6i	0.368259	+	0.637842i
$83$	2.65827e6			0.510301			0.255151	−	0.966901i	$-0.417875\pi$
$83$	2.65827e6			0.510301			0.255151	+	0.966901i	$0.417875\pi$
$84$	−1.56280e6	−	129451.i	−0.287690	−	0.0238301i
$85$	9.54818e6			1.68638
$86$	−1.82381e6	−	3.15892e6i	−0.309196	−	0.535543i
$87$	467797.	−	810248.i	0.0761623	−	0.131917i
$88$	−1.65969e6	+	2.87466e6i	−0.259619	+	0.449674i
$89$	686791.	+	1.18956e6i	0.103267	+	0.178863i	0.913029	−	0.407895i	$-0.133737\pi$
$89$	686791.	+	1.18956e6i	0.103267	+	0.178863i	−0.809762	+	0.586758i	$0.800404\pi$
$90$	1.80097e6			0.260410
$91$	513779.	−	741019.i	0.0714712	−	0.103082i
$92$	−5.19057e6			−0.694956
$93$	−2.16691e6	−	3.75319e6i	−0.279351	−	0.483850i
$94$	−1.19998e6	+	2.07842e6i	−0.149014	+	0.258099i
$95$	2.40705e6	−	4.16913e6i	0.288040	−	0.498899i
$96$	−442368.	−	766204.i	−0.0510310	−	0.0883883i
$97$	299539.			0.0333236			0.0166618	−	0.999861i	$-0.494696\pi$
$97$	299539.			0.0333236			0.0166618	+	0.999861i	$0.494696\pi$
$98$	−4.18807e6	+	5.08590e6i	−0.449492	+	0.545854i
$99$	4.72622e6			0.489543
$100$	−551601.	−	955401.i	−0.0551601	−	0.0955401i
$101$	−709804.	+	1.22942e6i	−0.0685509	+	0.118734i	−0.898264	−	0.439457i	$-0.855171\pi$
$101$	−709804.	+	1.22942e6i	−0.0685509	+	0.118734i	0.829713	+	0.558191i	$0.188504\pi$
$102$	−3.33930e6	+	5.78384e6i	−0.311570	+	0.539654i
$103$	−9.35929e6	−	1.62108e7i	−0.843942	−	1.46175i	−0.886537	−	0.462657i	$-0.846896\pi$
$103$	−9.35929e6	−	1.62108e7i	−0.843942	−	1.46175i	0.0425955	−	0.999092i	$-0.486437\pi$
$104$	508736.			0.0443482
$105$	4.31128e6	−	6.21812e6i	0.363449	−	0.524199i
$106$	1.51838e7			1.23825
$107$	−2.10297e6	−	3.64245e6i	−0.165955	−	0.287442i	0.771039	−	0.636788i	$-0.219737\pi$
$107$	−2.10297e6	−	3.64245e6i	−0.165955	−	0.287442i	−0.936994	+	0.349346i	$0.886404\pi$
$108$	−629856.	+	1.09094e6i	−0.0481125	+	0.0833333i
$109$	−5.45235e6	+	9.44375e6i	−0.403265	+	0.698476i	−0.994118	−	0.108303i	$-0.965458\pi$
$109$	−5.45235e6	+	9.44375e6i	−0.403265	+	0.698476i	0.590853	+	0.806780i	$0.298792\pi$
$110$	−8.00821e6	−	1.38706e7i	−0.573668	−	0.993623i
$111$	−299284.			−0.0207708
$112$	−3.70440e6	−	306846.i	−0.249147	−	0.0206375i
$113$	7.18622e6			0.468517			0.234259	−	0.972174i	$-0.424734\pi$
$113$	7.18622e6			0.468517			0.234259	+	0.972174i	$0.424734\pi$
$114$	1.68364e6	+	2.91615e6i	0.106435	+	0.184350i
$115$	1.25226e7	−	2.16897e7i	0.767806	−	1.32988i
$116$	1.10885e6	−	1.92059e6i	0.0659585	−	0.114243i
$117$	−362177.	−	627308.i	−0.0209059	−	0.0362102i
$118$	−2.37013e7			−1.32796
$119$	1.19757e7	+	2.53752e7i	0.651460	+	1.38037i
$120$	4.26897e6			0.225522
$121$	−1.12721e7	−	1.95238e7i	−0.578435	−	1.00188i
$122$	9.53484e6	−	1.65148e7i	0.475394	−	0.823407i
$123$	6.20548e6	−	1.07482e7i	0.300682	−	0.520796i
$124$	−5.13637e6	−	8.89645e6i	−0.241925	−	0.419026i
$125$	−1.88026e7			−0.861057
$126$	2.25885e6	+	4.78624e6i	0.100598	+	0.213156i
$127$	−1.62113e7			−0.702270			−0.351135	−	0.936325i	$-0.614204\pi$
$127$	−1.62113e7			−0.702270			−0.351135	+	0.936325i	$0.614204\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$	−6.15534e6	+	1.06614e7i	−0.252457	+	0.437269i
$130$	−1.22736e6	+	2.12585e6i	−0.0489971	+	0.0848654i
$131$	−3.37734e6	−	5.84973e6i	−0.131258	−	0.227346i	0.792904	−	0.609347i	$-0.208568\pi$
$131$	−3.37734e6	−	5.84973e6i	−0.131258	−	0.227346i	−0.924162	+	0.382001i	$0.875235\pi$
$132$	1.12029e7			0.423957
$133$	1.40989e7	+	1.16785e6i	0.519641	+	0.0430433i
$134$	3.62713e7			1.30226
$135$	−3.03914e6	−	5.26394e6i	−0.106312	−	0.184138i
$136$	−7.91538e6	+	1.37098e7i	−0.269827	+	0.467354i
$137$	−2.76387e7	+	4.78716e7i	−0.918322	+	1.59058i	−0.116359	+	0.993207i	$0.537122\pi$
$137$	−2.76387e7	+	4.78716e7i	−0.918322	+	1.59058i	−0.801963	+	0.597374i	$0.796211\pi$
$138$	8.75908e6	+	1.51712e7i	0.283715	+	0.491408i
$139$	−3.26212e7			−1.03026			−0.515132	−	0.857111i	$-0.672257\pi$
$139$	−3.26212e7			−1.03026			−0.515132	+	0.857111i	$0.672257\pi$
$140$	1.02193e7	−	1.47392e7i	0.314756	−	0.453970i
$141$	8.09985e6			0.243338
$142$	1.60279e7	+	2.77611e7i	0.469751	+	0.813632i
$143$	−3.22092e6	+	5.57879e6i	−0.0921092	+	0.159538i
$144$	−1.49299e6	+	2.58594e6i	−0.0416667	+	0.0721688i
$145$	5.35035e6	+	9.26708e6i	0.145745	+	0.252438i
$146$	−2.77848e7			−0.738877
$147$	2.19326e7	+	3.65858e6i	0.569482	+	0.0949953i
$148$	−709415.			−0.0179881
$149$	3.21298e7	+	5.56505e7i	0.795713	+	1.37822i	0.922386	+	0.386270i	$0.126237\pi$
$149$	3.21298e7	+	5.56505e7i	0.795713	+	1.37822i	−0.126673	+	0.991945i	$0.540430\pi$
$150$	−1.86165e6	+	3.22448e6i	−0.0450380	+	0.0780082i
$151$	−3.11266e7	+	5.39128e7i	−0.735719	+	1.27430i	0.218688	+	0.975795i	$0.429822\pi$
$151$	−3.11266e7	+	5.39128e7i	−0.735719	+	1.27430i	−0.954407	+	0.298508i	$0.903511\pi$
$152$	3.99086e6	+	6.91236e6i	0.0921751	+	0.159652i
$153$	2.25403e7			0.508791
$154$	2.68182e7	−	3.86797e7i	0.591708	−	0.853415i
$155$	4.95673e7			1.06914
$156$	−858493.	−	1.48695e6i	−0.0181051	−	0.0313589i
$157$	−8.89893e6	+	1.54134e7i	−0.183522	+	0.317870i	−0.943078	−	0.332573i	$-0.892083\pi$
$157$	−8.89893e6	+	1.54134e7i	−0.183522	+	0.317870i	0.759555	+	0.650443i	$0.225417\pi$
$158$	2.77147e6	−	4.80033e6i	0.0558999	−	0.0968214i
$159$	−2.56226e7	−	4.43797e7i	−0.505515	−	0.875577i
$160$	1.01190e7			0.195307
$161$	7.33488e7	+	6.07569e6i	1.38517	+	0.114737i
$162$	4.25153e6			0.0785674
$163$	−1.92169e7	−	3.32846e7i	−0.347557	−	0.601986i	0.638258	−	0.769823i	$-0.279655\pi$
$163$	−1.92169e7	−	3.32846e7i	−0.347557	−	0.601986i	−0.985815	+	0.167836i	$0.946322\pi$
$164$	1.47093e7	−	2.54772e7i	0.260398	−	0.451023i
$165$	−2.70277e7	+	4.68134e7i	−0.468398	+	0.811290i
$166$	−1.06331e7	−	1.84171e7i	−0.180419	−	0.312494i
$167$	−5.42631e7			−0.901566			−0.450783	−	0.892634i	$-0.648855\pi$
$167$	−5.42631e7			−0.901566			−0.450783	+	0.892634i	$0.648855\pi$
$168$	5.35432e6	+	1.13452e7i	0.0871208	+	0.184599i
$169$	−6.17612e7			−0.984266
$170$	−3.81927e7	−	6.61517e7i	−0.596224	−	1.03269i
$171$	5.68229e6	−	9.84202e6i	0.0869035	−	0.150521i
$172$	−1.45904e7	+	2.52714e7i	−0.218635	+	0.378686i
$173$	−8.55530e6	−	1.48182e7i	−0.125624	−	0.217588i	0.796352	−	0.604833i	$-0.206760\pi$
$173$	−8.55530e6	−	1.48182e7i	−0.125624	−	0.217588i	−0.921977	+	0.387245i	$0.873427\pi$
$174$	−7.48475e6			−0.107710
$175$	6.67645e6	+	1.41466e7i	0.0941700	+	0.199535i
$176$	2.65550e7			0.367157
$177$	3.99960e7	+	6.92751e7i	0.542138	+	0.939011i
$178$	5.49433e6	−	9.51646e6i	0.0730205	−	0.126475i
$179$	3.20119e7	−	5.54463e7i	0.417182	−	0.722581i	−0.578472	−	0.815702i	$-0.696351\pi$
$179$	3.20119e7	−	5.54463e7i	0.417182	−	0.722581i	0.995655	+	0.0931208i	$0.0296843\pi$
$180$	−7.20388e6	−	1.24775e7i	−0.0920688	−	0.159468i
$181$	6.60928e6			0.0828475			0.0414237	−	0.999142i	$-0.486811\pi$
$181$	6.60928e6			0.0828475			0.0414237	+	0.999142i	$0.486811\pi$
$182$	−7.18904e6	−	595488.i	−0.0883937	−	0.00732189i
$183$	−6.43601e7			−0.776315
$184$	2.07623e7	+	3.59613e7i	0.245704	+	0.425572i
$185$	1.71151e6	−	2.96442e6i	0.0198737	−	0.0344222i
$186$	−1.73352e7	+	3.00255e7i	−0.197531	+	0.342133i
$187$	−1.00228e8	−	1.73600e8i	−1.12084	−	1.94135i
$188$	1.91996e7			0.210737
$189$	1.01776e7	−	1.46790e7i	0.109655	−	0.158154i
$190$	−3.85128e7			−0.407350
$191$	−1.13085e7	−	1.95869e7i	−0.117432	−	0.203399i	0.801317	−	0.598240i	$-0.204133\pi$
$191$	−1.13085e7	−	1.95869e7i	−0.117432	−	0.203399i	−0.918749	+	0.394841i	$0.870800\pi$
$192$	−3.53894e6	+	6.12963e6i	−0.0360844	+	0.0625000i
$193$	−8.00169e6	+	1.38593e7i	−0.0801182	+	0.138769i	−0.903301	−	0.429008i	$-0.858863\pi$
$193$	−8.00169e6	+	1.38593e7i	−0.0801182	+	0.138769i	0.823182	+	0.567777i	$0.192196\pi$
$194$	−1.19816e6	−	2.07527e6i	−0.0117817	−	0.0204065i
$195$	8.28468e6			0.0800119
$196$	5.19884e7	+	8.67219e6i	0.493185	+	0.0822683i
$197$	−1.29465e7			−0.120648			−0.0603242	−	0.998179i	$-0.519213\pi$
$197$	−1.29465e7			−0.120648			−0.0603242	+	0.998179i	$0.519213\pi$
$198$	−1.89049e7	−	3.27442e7i	−0.173080	−	0.299783i
$199$	1.01406e8	−	1.75640e8i	0.912173	−	1.57993i	0.101184	−	0.994868i	$-0.467737\pi$
$199$	1.01406e8	−	1.75640e8i	0.912173	−	1.57993i	0.810989	−	0.585062i	$-0.198930\pi$
$200$	−4.41281e6	+	7.64321e6i	−0.0390041	+	0.0675571i
$201$	−6.12079e7	−	1.06015e8i	−0.531644	−	0.920835i
$202$	1.13569e7			0.0969457
$203$	−1.79175e7	+	2.58422e7i	−0.150328	+	0.216817i
$204$	5.34288e7			0.440626
$205$	7.09741e7	+	1.22931e8i	0.575389	+	0.996603i
$206$	−7.48743e7	+	1.29686e8i	−0.596757	+	1.03361i
$207$	2.95619e7	−	5.12027e7i	0.231652	−	0.401233i
$208$	−2.03495e6	−	3.52463e6i	−0.0156795	−	0.0271576i
$209$	−1.01068e8			−0.765774
$210$	−6.03255e7	−	4.99693e6i	−0.449504	−	0.0372337i
$211$	2.54584e8			1.86570			0.932851	−	0.360262i	$-0.117313\pi$
$211$	2.54584e8			1.86570			0.932851	+	0.360262i	$0.117313\pi$
$212$	−6.07351e7	−	1.05196e8i	−0.437789	−	0.758272i
$213$	5.40942e7	−	9.36938e7i	0.383550	−	0.664328i
$214$	−1.68237e7	+	2.91396e7i	−0.117348	+	0.203252i
$215$	−7.04008e7	−	1.21938e8i	−0.483106	−	0.836765i
$216$	1.00777e7			0.0680414
$217$	6.21694e7	+	1.31730e8i	0.413017	+	0.875133i
$218$	8.72376e7			0.570303
$219$	4.68868e7	+	8.12104e7i	0.301645	+	0.522465i
$220$	−6.40657e7	+	1.10965e8i	−0.405645	+	0.702597i
$221$	−1.53612e7	+	2.66063e7i	−0.0957308	+	0.165811i
$222$	1.19714e6	+	2.07350e6i	0.00734360	+	0.0127195i
$223$	1.97491e8			1.19256			0.596280	−	0.802777i	$-0.296645\pi$
$223$	1.97491e8			1.19256			0.596280	+	0.802777i	$0.296645\pi$
$224$	1.26917e7	+	2.68922e7i	0.0754488	+	0.159867i
$225$	1.25662e7			0.0735468
$226$	−2.87449e7	−	4.97876e7i	−0.165646	−	0.286907i
$227$	−3.09513e7	+	5.36092e7i	−0.175626	+	0.304193i	−0.940378	−	0.340132i	$-0.889528\pi$
$227$	−3.09513e7	+	5.36092e7i	−0.175626	+	0.304193i	0.764752	+	0.644325i	$0.222862\pi$
$228$	1.34691e7	−	2.33292e7i	0.0752606	−	0.130355i
$229$	1.55203e8	+	2.68819e8i	0.854035	+	1.47923i	0.877537	+	0.479509i	$0.159185\pi$
$229$	1.55203e8	+	2.68819e8i	0.854035	+	1.47923i	−0.0235015	+	0.999724i	$0.507481\pi$
$230$	−2.00361e8			−1.08584
$231$	−1.58310e8	−	1.31133e7i	−0.845019	−	0.0699953i
$232$	−1.77416e7			−0.0932794
$233$	−6.17555e7	−	1.06964e8i	−0.319838	−	0.553976i	0.660616	−	0.750724i	$-0.270295\pi$
$233$	−6.17555e7	−	1.06964e8i	−0.319838	−	0.553976i	−0.980454	+	0.196748i	$0.936962\pi$
$234$	−2.89741e6	+	5.01847e6i	−0.0147827	+	0.0256045i
$235$	−4.63204e7	+	8.02293e7i	−0.232828	+	0.403269i
$236$	9.48053e7	+	1.64208e8i	0.469505	+	0.813207i
$237$	−1.87074e7			−0.0912841
$238$	1.27901e8	−	1.84471e8i	0.614973	−	0.886970i
$239$	1.86771e8			0.884944			0.442472	−	0.896782i	$-0.354102\pi$
$239$	1.86771e8			0.884944			0.442472	+	0.896782i	$0.354102\pi$
$240$	−1.70759e7	−	2.95763e7i	−0.0797339	−	0.138103i
$241$	5.46575e7	−	9.46695e7i	0.251530	−	0.435663i	−0.712417	−	0.701756i	$-0.752400\pi$
$241$	5.46575e7	−	9.46695e7i	0.251530	−	0.435663i	0.963947	+	0.266093i	$0.0857329\pi$
$242$	−9.01765e7	+	1.56190e8i	−0.409016	+	0.708436i
$243$	−7.17445e6	−	1.24265e7i	−0.0320750	−	0.0555556i
$244$	−1.52557e8			−0.672309
$245$	−1.61664e8	+	1.96321e8i	−0.702314	+	0.852875i
$246$	−9.92876e7			−0.425228
$247$	7.74495e6	+	1.34147e7i	0.0327024	+	0.0566422i
$248$	−4.10910e7	+	7.11716e7i	−0.171067	+	0.296296i
$249$	−3.58867e7	+	6.21576e7i	−0.147311	+	0.255151i
$250$	7.52102e7	+	1.30268e8i	0.304430	+	0.527287i
$251$	−1.32241e8			−0.527846			−0.263923	−	0.964544i	$-0.585016\pi$
$251$	−1.32241e8			−0.527846			−0.263923	+	0.964544i	$0.585016\pi$
$252$	2.41246e7	−	3.47948e7i	0.0949640	−	0.136966i
$253$	−5.25801e8			−2.04127
$254$	6.48451e7	+	1.12315e8i	0.248290	+	0.430051i
$255$	−1.28900e8	+	2.23262e8i	−0.486815	+	0.843188i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	6.22242e7	+	1.07775e8i	0.228662	+	0.396053i	0.957412	−	0.288726i	$-0.0932318\pi$
$257$	6.22242e7	+	1.07775e8i	0.228662	+	0.396053i	−0.728750	+	0.684780i	$0.759898\pi$
$258$	9.84855e7			0.357029
$259$	1.00249e7	+	830388.i	0.0358533	+	0.00296983i
$260$	1.96377e7			0.0692923
$261$	1.26305e7	+	2.18767e7i	0.0439723	+	0.0761623i
$262$	−2.70188e7	+	4.67979e7i	−0.0928134	+	0.160758i
$263$	2.43121e8	−	4.21098e8i	0.824095	−	1.42737i	−0.0785143	−	0.996913i	$-0.525018\pi$
$263$	2.43121e8	−	4.21098e8i	0.824095	−	1.42737i	0.902609	−	0.430461i	$-0.141649\pi$
$264$	−4.48116e7	−	7.76159e7i	−0.149891	−	0.259619i
$265$	5.86110e8			1.93472
$266$	−4.83044e7	−	1.02351e8i	−0.157362	−	0.333432i
$267$	−3.70867e7			−0.119242
$268$	−1.45085e8	−	2.51295e8i	−0.460417	−	0.797466i
$269$	2.90735e8	−	5.03568e8i	0.910676	−	1.57734i	0.0975655	−	0.995229i	$-0.468894\pi$
$269$	2.90735e8	−	5.03568e8i	0.910676	−	1.57734i	0.813111	−	0.582109i	$-0.197772\pi$
$270$	−2.43131e7	+	4.21115e7i	−0.0751739	+	0.130205i
$271$	1.20919e8	+	2.09437e8i	0.369064	+	0.639237i	0.989419	−	0.145084i	$-0.0463451\pi$
$271$	1.20919e8	+	2.09437e8i	0.369064	+	0.639237i	−0.620356	+	0.784321i	$0.713012\pi$
$272$	1.26646e8			0.381593
$273$	1.03910e7	+	2.20173e7i	0.0309092	+	0.0654929i
$274$	4.42219e8			1.29870
$275$	−5.58768e7	−	9.67815e7i	−0.162019	−	0.280626i
$276$	7.00727e7	−	1.21369e8i	0.200617	−	0.347478i
$277$	−1.23766e8	+	2.14369e8i	−0.349882	+	0.606013i	−0.986228	−	0.165390i	$-0.947112\pi$
$277$	−1.23766e8	+	2.14369e8i	−0.349882	+	0.606013i	0.636346	+	0.771403i	$0.280445\pi$
$278$	1.30485e8	+	2.26007e8i	0.364254	+	0.630906i
$279$	1.17013e8			0.322566
$280$	−1.42994e8	−	1.18446e7i	−0.389282	−	0.0322453i
$281$	−3.68601e8			−0.991026			−0.495513	−	0.868601i	$-0.665020\pi$
$281$	−3.68601e8			−0.991026			−0.495513	+	0.868601i	$0.665020\pi$
$282$	−3.23994e7	−	5.61174e7i	−0.0860330	−	0.149014i
$283$	−8.30769e7	+	1.43893e8i	−0.217885	+	0.377388i	−0.954161	−	0.299293i	$-0.903249\pi$
$283$	−8.30769e7	+	1.43893e8i	−0.217885	+	0.377388i	0.736276	+	0.676681i	$0.236583\pi$
$284$	1.28223e8	−	2.22089e8i	0.332164	−	0.575325i
$285$	6.49903e7	+	1.12567e8i	0.166300	+	0.288040i
$286$	5.15346e7			0.130262
$287$	−2.37681e8	+	3.42805e8i	−0.593483	+	0.855975i
$288$	2.38879e7			0.0589256
$289$	−2.72837e8	−	4.72567e8i	−0.664907	−	1.15165i
$290$	4.28028e7	−	7.41367e7i	0.103057	−	0.178501i
$291$	−4.04378e6	+	7.00403e6i	−0.00961970	+	0.0166618i
$292$	1.11139e8	+	1.92499e8i	0.261233	+	0.452468i
$293$	−2.64915e7			−0.0615276			−0.0307638	−	0.999527i	$-0.509794\pi$
$293$	−2.64915e7			−0.0615276			−0.0307638	+	0.999527i	$0.509794\pi$
$294$	−6.23831e7	−	1.66588e8i	−0.143170	−	0.382321i
$295$	−9.14896e8			−2.07489
$296$	2.83766e6	+	4.91497e6i	0.00635974	+	0.0110154i
$297$	−6.38040e7	+	1.10512e8i	−0.141319	+	0.244771i
$298$	2.57039e8	−	4.45204e8i	0.562654	−	0.974545i
$299$	4.02928e7	+	6.97892e7i	0.0871723	+	0.150987i
$300$	2.97865e7			0.0636934
$301$	2.35761e8	−	3.40036e8i	0.498298	−	0.718691i
$302$	4.98025e8			1.04046
$303$	−1.91647e7	−	3.31942e7i	−0.0395779	−	0.0685509i
$304$	3.19268e7	−	5.52989e7i	0.0651776	−	0.112891i
$305$	3.68054e8	−	6.37489e8i	0.742784	−	1.28654i
$306$	−9.01611e7	−	1.56164e8i	−0.179885	−	0.311570i
$307$	−7.09759e8			−1.39999			−0.699997	−	0.714146i	$-0.746815\pi$
$307$	−7.09759e8			−1.39999			−0.699997	+	0.714146i	$0.746815\pi$
$308$	−3.75253e8	−	3.10833e7i	−0.731808	−	0.0606177i
$309$	5.05401e8			0.974500
$310$	−1.98269e8	−	3.43412e8i	−0.377998	−	0.654711i
$311$	−2.11645e7	+	3.66581e7i	−0.0398977	+	0.0691048i	−0.885285	−	0.465049i	$-0.846037\pi$
$311$	−2.11645e7	+	3.66581e7i	−0.0398977	+	0.0691048i	0.845387	+	0.534154i	$0.179370\pi$
$312$	−6.86794e6	+	1.18956e7i	−0.0128022	+	0.0221741i
$313$	4.05048e6	+	7.01564e6i	0.00746623	+	0.0129319i	0.869734	−	0.493520i	$-0.164290\pi$
$313$	4.05048e6	+	7.01564e6i	0.00746623	+	0.0129319i	−0.862268	+	0.506452i	$0.830957\pi$
$314$	1.42383e8			0.259540
$315$	8.71941e7	+	1.84754e8i	0.157181	+	0.333048i
$316$	−4.43435e7			−0.0790543
$317$	2.37441e8	+	4.11260e8i	0.418648	+	0.725119i	0.995804	−	0.0915148i	$-0.0291709\pi$
$317$	2.37441e8	+	4.11260e8i	0.418648	+	0.725119i	−0.577156	+	0.816634i	$0.695838\pi$
$318$	−2.04981e8	+	3.55038e8i	−0.357453	+	0.619127i
$319$	1.12326e8	−	1.94554e8i	0.193737	−	0.335562i
$320$	−4.04761e7	−	7.01067e7i	−0.0690516	−	0.119601i
$321$	1.13560e8			0.191628
$322$	−2.51302e8	−	5.32478e8i	−0.419469	−	0.888805i
$323$	−4.82012e8			−0.795883
$324$	−1.70061e7	−	2.94555e7i	−0.0277778	−	0.0481125i
$325$	−8.56383e6	+	1.48330e7i	−0.0138381	+	0.0239683i
$326$	−1.53735e8	+	2.66277e8i	−0.245760	+	0.425669i
$327$	−1.47213e8	−	2.54981e8i	−0.232825	−	0.403265i
$328$	−2.35348e8			−0.368259
$329$	−2.71314e8	−	2.24737e7i	−0.420035	−	0.0347927i
$330$	4.32443e8			0.662415
$331$	4.55018e8	+	7.88114e8i	0.689653	+	1.19451i	0.971950	+	0.235186i	$0.0755700\pi$
$331$	4.55018e8	+	7.88114e8i	0.689653	+	1.19451i	−0.282298	+	0.959327i	$0.591097\pi$
$332$	−8.50648e7	+	1.47337e8i	−0.127575	+	0.220967i
$333$	4.04034e6	−	6.99807e6i	0.00599602	−	0.0103854i
$334$	2.17053e8	+	3.75946e8i	0.318752	+	0.552094i
$335$	1.40011e9			2.03472
$336$	5.71843e7	−	8.24765e7i	0.0822412	−	0.118616i
$337$	−1.34422e9			−1.91323			−0.956614	−	0.291359i	$-0.905893\pi$
$337$	−1.34422e9			−1.91323			−0.956614	+	0.291359i	$0.905893\pi$
$338$	2.47045e8	+	4.27894e8i	0.347991	+	0.602737i
$339$	−9.70139e7	+	1.68033e8i	−0.135249	+	0.234259i
$340$	−3.05542e8	+	5.29214e8i	−0.421594	+	0.730222i
$341$	−5.20311e8	−	9.01205e8i	−0.710595	−	1.23079i
$342$	−9.09167e7			−0.122900
$343$	−7.24506e8	−	1.83402e8i	−0.969422	−	0.245400i
$344$	2.33447e8			0.309196
$345$	3.38110e8	+	5.85623e8i	0.443293	+	0.767806i
$346$	−6.84424e7	+	1.18546e8i	−0.0888298	+	0.153858i
$347$	2.38413e8	−	4.12943e8i	0.306320	−	0.530563i	−0.671234	−	0.741246i	$-0.734235\pi$
$347$	2.38413e8	−	4.12943e8i	0.306320	−	0.530563i	0.977554	+	0.210683i	$0.0675688\pi$
$348$	2.99390e7	+	5.18559e7i	0.0380811	+	0.0659585i
$349$	9.67291e8			1.21806			0.609029	−	0.793148i	$-0.291559\pi$
$349$	9.67291e8			1.21806			0.609029	+	0.793148i	$0.291559\pi$
$350$	7.13047e7	−	1.02842e8i	0.0888956	−	0.128213i
$351$	1.95575e7			0.0241401
$352$	−1.06220e8	−	1.83978e8i	−0.129810	−	0.224837i
$353$	−3.41483e8	+	5.91465e8i	−0.413197	+	0.715678i	−0.995237	−	0.0974819i	$-0.968921\pi$
$353$	−3.41483e8	+	5.91465e8i	−0.413197	+	0.715678i	0.582040	+	0.813160i	$0.302255\pi$
$354$	3.19968e8	−	5.54201e8i	0.383350	−	0.663981i
$355$	6.18693e8	+	1.07161e9i	0.733967	+	1.27127i
$356$	−8.79093e7			−0.103267
$357$	−7.55012e8	−	6.25397e7i	−0.878244	−	0.0727474i
$358$	−5.12191e8			−0.589985
$359$	5.63400e8	+	9.75838e8i	0.642668	+	1.11313i	0.984835	+	0.173494i	$0.0555057\pi$
$359$	5.63400e8	+	9.75838e8i	0.642668	+	1.11313i	−0.342167	+	0.939639i	$0.611161\pi$
$360$	−5.76310e7	+	9.98199e7i	−0.0651025	+	0.112761i
$361$	3.25423e8	−	5.63649e8i	0.364060	−	0.630571i
$362$	−2.64371e7	−	4.57904e7i	−0.0292910	−	0.0507335i
$363$	6.08692e8			0.667920
$364$	2.46305e7	+	5.21891e7i	0.0267682	+	0.0567185i
$365$	−1.07252e9			−1.15447
$366$	2.57441e8	+	4.45900e8i	0.274469	+	0.475394i
$367$	5.12152e8	−	8.87073e8i	0.540838	−	0.936760i	−0.458018	−	0.888943i	$-0.651440\pi$
$367$	5.12152e8	−	8.87073e8i	0.540838	−	0.936760i	0.998856	−	0.0478166i	$-0.0152263\pi$
$368$	1.66098e8	−	2.87690e8i	0.173739	−	0.300925i
$369$	1.67548e8	+	2.90201e8i	0.173599	+	0.300682i
$370$	−2.73842e7			−0.0281056
$371$	7.35124e8	+	1.55764e9i	0.747398	+	1.58365i
$372$	2.77364e8			0.279351
$373$	3.50582e8	+	6.07226e8i	0.349791	+	0.605856i	0.986212	−	0.165486i	$-0.0529193\pi$
$373$	3.50582e8	+	6.07226e8i	0.349791	+	0.605856i	−0.636421	+	0.771342i	$0.719586\pi$
$374$	−8.01823e8	+	1.38880e9i	−0.792552	+	1.37274i
$375$	2.53834e8	−	4.39654e8i	0.248566	−	0.430528i
$376$	−7.67986e7	−	1.33019e8i	−0.0745068	−	0.129050i
$377$	−3.44307e7			−0.0330942
$378$	−1.42410e8	−	1.17962e7i	−0.135618	−	0.0112336i
$379$	3.40034e8			0.320838			0.160419	−	0.987049i	$-0.448715\pi$
$379$	3.40034e8			0.320838			0.160419	+	0.987049i	$0.448715\pi$
$380$	1.54051e8	+	2.66824e8i	0.144020	+	0.249450i
$381$	2.18852e8	−	3.79063e8i	0.202728	−	0.351135i
$382$	−9.04679e7	+	1.56695e8i	−0.0830372	+	0.143825i
$383$	4.29964e8	+	7.44719e8i	0.391053	+	0.677324i	0.992589	−	0.121522i	$-0.0387775\pi$
$383$	4.29964e8	+	7.44719e8i	0.391053	+	0.677324i	−0.601535	+	0.798846i	$0.705444\pi$
$384$	5.66231e7			0.0510310
$385$	1.03521e9	−	1.49308e9i	0.924520	−	1.33343i
$386$	1.28027e8			0.113304
$387$	−1.66194e8	−	2.87857e8i	−0.145756	−	0.252457i
$388$	−9.58525e6	+	1.66021e7i	−0.00833091	+	0.0144296i
$389$	−9.65248e6	+	1.67186e7i	−0.00831410	+	0.0144004i	−0.870153	−	0.492782i	$-0.835980\pi$
$389$	−9.65248e6	+	1.67186e7i	−0.00831410	+	0.0144004i	0.861838	+	0.507183i	$0.169313\pi$
$390$	−3.31387e7	−	5.73979e7i	−0.0282885	−	0.0489971i
$391$	−2.50765e9			−2.12152
$392$	−1.47871e8	−	3.94875e8i	−0.123989	−	0.331099i
$393$	1.82377e8			0.151564
$394$	5.17862e7	+	8.96963e7i	0.0426557	+	0.0738818i
$395$	1.06982e8	−	1.85298e8i	0.0873413	−	0.151280i
$396$	−1.51239e8	+	2.61954e8i	−0.122386	+	0.211978i
$397$	3.26680e8	+	5.65827e8i	0.262033	+	0.453855i	0.966782	−	0.255602i	$-0.0822737\pi$
$397$	3.26680e8	+	5.65827e8i	0.262033	+	0.453855i	−0.704749	+	0.709457i	$0.748940\pi$
$398$	−1.62249e9			−1.29001
$399$	−2.17642e8	+	3.13904e8i	−0.171529	+	0.247395i
$400$	7.06049e7			0.0551601
$401$	−8.65527e8	−	1.49914e9i	−0.670309	−	1.16101i	−0.977816	−	0.209464i	$-0.932828\pi$
$401$	−8.65527e8	−	1.49914e9i	−0.670309	−	1.16101i	0.307507	−	0.951546i	$-0.400505\pi$
$402$	−4.89663e8	+	8.48121e8i	−0.375929	+	0.651128i
$403$	−7.97442e7	+	1.38121e8i	−0.0606920	+	0.105122i
$404$	−4.54274e7	−	7.86826e7i	−0.0342755	−	0.0593669i
$405$	1.64113e8			0.122758
$406$	2.50710e8	+	2.07670e7i	0.185922	+	0.0154004i
$407$	−7.18633e7			−0.0528356
$408$	−2.13715e8	−	3.70166e8i	−0.155785	−	0.269827i
$409$	8.98363e8	−	1.55601e9i	0.649262	−	1.12456i	−0.334037	−	0.942560i	$-0.608411\pi$
$409$	8.98363e8	−	1.55601e9i	0.649262	−	1.12456i	0.983299	−	0.181996i	$-0.0582557\pi$
$410$	5.67793e8	−	9.83447e8i	0.406862	−	0.704705i
$411$	−7.46244e8	−	1.29253e9i	−0.530194	−	0.918322i
$412$	1.19799e9			0.843942
$413$	−1.14750e9	−	2.43142e9i	−0.801545	−	1.69838i
$414$	−4.72990e8			−0.327606
$415$	−4.10448e8	−	7.10918e8i	−0.281897	−	0.488260i
$416$	−1.62796e7	+	2.81970e7i	−0.0110871	+	0.0192033i
$417$	4.40387e8	−	7.62772e8i	0.297412	−	0.515132i
$418$	4.04271e8	+	7.00218e8i	0.270742	+	0.468939i
$419$	1.18733e9			0.788536			0.394268	−	0.918995i	$-0.370998\pi$
$419$	1.18733e9			0.788536			0.394268	+	0.918995i	$0.370998\pi$
$420$	2.06682e8	+	4.37935e8i	0.136123	+	0.288428i
$421$	−3.66435e8			−0.239337			−0.119669	−	0.992814i	$-0.538183\pi$
$421$	−3.66435e8			−0.239337			−0.119669	+	0.992814i	$0.538183\pi$
$422$	−1.01834e9	−	1.76381e9i	−0.659625	−	1.14250i
$423$	−1.09348e8	+	1.89396e8i	−0.0702457	+	0.121669i
$424$	−4.85881e8	+	8.41571e8i	−0.309563	+	0.536179i
$425$	−2.66488e8	−	4.61570e8i	−0.168390	−	0.291660i
$426$	−8.65507e8			−0.542421
$427$	2.15582e9	+	1.78572e8i	1.34003	+	0.110998i
$428$	2.69180e8			0.165955
$429$	−8.69647e7	−	1.50627e8i	−0.0531793	−	0.0921092i
$430$	−5.63206e8	+	9.75502e8i	−0.341608	+	0.591682i
$431$	3.26720e7	−	5.65896e7i	0.0196565	−	0.0340460i	−0.856030	−	0.516926i	$-0.827076\pi$
$431$	3.26720e7	−	5.65896e7i	0.0196565	−	0.0340460i	0.875686	+	0.482880i	$0.160409\pi$
$432$	−4.03108e7	−	6.98203e7i	−0.0240563	−	0.0416667i
$433$	−1.55564e9			−0.920874			−0.460437	−	0.887692i	$-0.652307\pi$
$433$	−1.55564e9			−0.920874			−0.460437	+	0.887692i	$0.652307\pi$
$434$	6.63972e8	−	9.57641e8i	0.389884	−	0.562327i
$435$	−2.88919e8			−0.168292
$436$	−3.48950e8	−	6.04400e8i	−0.201633	−	0.349238i
$437$	−6.32166e8	+	1.09494e9i	−0.362365	+	0.627634i
$438$	3.75095e8	−	6.49683e8i	0.213295	−	0.369439i
$439$	1.33630e9	+	2.31454e9i	0.753839	+	1.30569i	0.945950	+	0.324314i	$0.105133\pi$
$439$	1.33630e9	+	2.31454e9i	0.753839	+	1.30569i	−0.192111	+	0.981373i	$0.561533\pi$
$440$	1.02505e9			0.573668
$441$	−3.81638e8	+	4.63453e8i	−0.211893	+	0.257318i
$442$	2.45779e8			0.135384
$443$	1.17317e9	+	2.03199e9i	0.641133	+	1.11048i	0.985180	+	0.171523i	$0.0548687\pi$
$443$	1.17317e9	+	2.03199e9i	0.641133	+	1.11048i	−0.344047	+	0.938952i	$0.611798\pi$
$444$	9.57710e6	−	1.65880e7i	0.00519271	−	0.00899403i
$445$	2.12087e8	−	3.67345e8i	0.114092	−	0.197612i
$446$	−7.89964e8	−	1.36826e9i	−0.421633	−	0.730291i
$447$	−1.73501e9			−0.918810
$448$	1.35548e8	−	1.95500e8i	0.0712230	−	0.102724i
$449$	2.07584e9			1.08226			0.541129	−	0.840940i	$-0.317997\pi$
$449$	2.07584e9			1.08226			0.541129	+	0.840940i	$0.317997\pi$
$450$	−5.02646e7	−	8.70609e7i	−0.0260027	−	0.0450380i
$451$	1.49004e9	−	2.58082e9i	0.764856	−	1.32477i
$452$	−2.29959e8	+	3.98300e8i	−0.117129	+	0.202874i
$453$	−8.40417e8	−	1.45565e9i	−0.424768	−	0.735719i
$454$	4.95220e8			0.248372
$455$	−2.77505e8	−	2.29865e7i	−0.138112	−	0.0114402i
$456$	−2.15506e8			−0.106435
$457$	8.35072e8	+	1.44639e9i	0.409277	+	0.708889i	0.994809	−	0.101761i	$-0.0324476\pi$
$457$	8.35072e8	+	1.44639e9i	0.409277	+	0.708889i	−0.585532	+	0.810649i	$0.699114\pi$
$458$	1.24162e9	−	2.15056e9i	0.603894	−	1.04598i
$459$	−3.04294e8	+	5.27052e8i	−0.146875	+	0.254395i
$460$	8.01445e8	+	1.38814e9i	0.383903	+	0.664939i
$461$	−1.80273e8			−0.0856995			−0.0428498	−	0.999082i	$-0.513644\pi$
$461$	−1.80273e8			−0.0856995			−0.0428498	+	0.999082i	$0.513644\pi$
$462$	5.42389e8	+	1.14926e9i	0.255896	+	0.542214i
$463$	−2.76184e9			−1.29320			−0.646598	−	0.762831i	$-0.723809\pi$
$463$	−2.76184e9			−1.29320			−0.646598	+	0.762831i	$0.723809\pi$
$464$	7.09665e7	+	1.22918e8i	0.0329792	+	0.0571217i
$465$	−6.69158e8	+	1.15902e9i	−0.308634	+	0.534570i
$466$	−4.94044e8	+	8.55710e8i	−0.226160	+	0.391720i
$467$	−1.22566e9	−	2.12291e9i	−0.556880	−	0.964545i	−0.997755	−	0.0669761i	$-0.978665\pi$
$467$	−1.22566e9	−	2.12291e9i	−0.556880	−	0.964545i	0.440874	−	0.897569i	$-0.354668\pi$
$468$	4.63586e7			0.0209059
$469$	1.75608e9	+	3.72092e9i	0.786030	+	1.66550i
$470$	7.41126e8			0.329268
$471$	−2.40271e8	−	4.16162e8i	−0.105957	−	0.183522i
$472$	7.58442e8	−	1.31366e9i	0.331991	−	0.575024i
$473$	−1.47800e9	+	2.55997e9i	−0.642186	+	1.11230i
$474$	7.48297e7	+	1.29609e8i	0.0322738	+	0.0558999i
$475$	−2.68721e8			−0.115047
$476$	−1.78966e9	−	1.48242e8i	−0.760582	−	0.0630011i
$477$	1.38362e9			0.583718
$478$	−7.47083e8	−	1.29399e9i	−0.312875	−	0.541916i
$479$	−1.71553e9	+	2.97138e9i	−0.713220	+	1.23533i	0.250422	+	0.968137i	$0.419431\pi$
$479$	−1.71553e9	+	2.97138e9i	−0.713220	+	1.23533i	−0.963642	+	0.267197i	$0.913903\pi$
$480$	−1.36607e8	+	2.36610e8i	−0.0563804	+	0.0976537i
$481$	5.50698e6	+	9.53836e6i	0.00225634	+	0.00390810i
$482$	−8.74520e8			−0.355717
$483$	−1.13228e9	+	1.63307e9i	−0.457232	+	0.659462i
$484$	1.44282e9			0.578435
$485$	−4.62501e7	−	8.01075e7i	−0.0184084	−	0.0318843i
$486$	−5.73956e7	+	9.94121e7i	−0.0226805	+	0.0392837i
$487$	−9.49694e8	+	1.64492e9i	−0.372591	+	0.645346i	−0.989963	−	0.141325i	$-0.954864\pi$
$487$	−9.49694e8	+	1.64492e9i	−0.372591	+	0.645346i	0.617372	+	0.786671i	$0.288197\pi$
$488$	6.10230e8	+	1.05695e9i	0.237697	+	0.411703i
$489$	1.03771e9			0.401324
$490$	2.00681e9	+	3.34755e8i	0.770583	+	0.128541i
$491$	5.21957e9			1.98998			0.994991	−	0.0999634i	$-0.0318726\pi$
$491$	5.21957e9			1.98998			0.994991	+	0.0999634i	$0.0318726\pi$
$492$	3.97150e8	+	6.87885e8i	0.150341	+	0.260398i
$493$	5.35705e8	−	9.27868e8i	0.201354	−	0.348756i
$494$	6.19596e7	−	1.07317e8i	0.0231241	−	0.0400521i
$495$	−7.29748e8	−	1.26396e9i	−0.270430	−	0.468398i
$496$	6.57455e8			0.241925
$497$	−2.07191e9	+	2.98829e9i	−0.757047	+	1.09188i
$498$	5.74187e8			0.208330
$499$	−8.59078e8	−	1.48797e9i	−0.309514	−	0.536095i	0.668742	−	0.743495i	$-0.266833\pi$
$499$	−8.59078e8	−	1.48797e9i	−0.309514	−	0.536095i	−0.978256	+	0.207400i	$0.933500\pi$
$500$	6.01682e8	−	1.04214e9i	0.215264	−	0.372848i
$501$	7.32552e8	−	1.26882e9i	0.260260	−	0.450783i
$502$	5.28963e8	+	9.16190e8i	0.186622	+	0.323238i
$503$	−1.00189e9			−0.351020			−0.175510	−	0.984478i	$-0.556157\pi$
$503$	−1.00189e9			−0.351020			−0.175510	+	0.984478i	$0.556157\pi$
$504$	−3.37564e8	−	2.79613e7i	−0.117449	−	0.00972862i
$505$	4.38386e8			0.151474
$506$	2.10320e9	+	3.64286e9i	0.721696	+	1.25001i
$507$	8.33777e8	−	1.44414e9i	0.284133	−	0.492133i
$508$	5.18761e8	−	8.98520e8i	0.175568	−	0.304092i
$509$	−1.97093e9	−	3.41376e9i	−0.662461	−	1.14742i	−0.979967	−	0.199159i	$-0.936179\pi$
$509$	−1.97093e9	−	3.41376e9i	−0.662461	−	1.14742i	0.317507	−	0.948256i	$-0.397154\pi$
$510$	2.06241e9			0.688460
$511$	−1.34520e9	−	2.85032e9i	−0.445979	−	0.944977i
$512$	1.34218e8			0.0441942
$513$	1.53422e8	+	2.65735e8i	0.0501737	+	0.0869035i
$514$	4.97793e8	−	8.62203e8i	0.161688	−	0.280052i
$515$	−2.89022e9	+	5.00602e9i	−0.932409	+	1.61498i
$516$	−3.93942e8	−	6.82327e8i	−0.126229	−	0.218635i
$517$	1.94491e9			0.618989
$518$	−3.43464e7	−	7.27759e7i	−0.0108574	−	0.0230056i
$519$	4.61986e8			0.145059
$520$	−7.85510e7	−	1.36054e8i	−0.0244985	−	0.0424327i
$521$	−1.90088e9	+	3.29241e9i	−0.588873	+	1.01996i	0.405507	+	0.914092i	$0.367095\pi$
$521$	−1.90088e9	+	3.29241e9i	−0.588873	+	1.01996i	−0.994380	+	0.105867i	$0.966238\pi$
$522$	1.01044e8	−	1.75014e8i	0.0310931	−	0.0538549i
$523$	8.92625e8	+	1.54607e9i	0.272843	+	0.472578i	0.969589	−	0.244740i	$-0.0787026\pi$
$523$	8.92625e8	+	1.54607e9i	0.272843	+	0.472578i	−0.696745	+	0.717318i	$0.745369\pi$
$524$	4.32300e8			0.131258
$525$	−4.20918e8	−	3.48658e7i	−0.126952	−	0.0105158i
$526$	−3.88993e9			−1.16545
$527$	−2.48146e9	−	4.29802e9i	−0.738535	−	1.27918i
$528$	−3.58493e8	+	6.20927e8i	−0.105989	+	0.183579i
$529$	−1.58640e9	+	2.74773e9i	−0.465928	+	0.807012i
$530$	−2.34444e9	−	4.06069e9i	−0.684027	−	1.18477i
$531$	−2.15978e9			−0.626007
$532$	−5.15893e8	+	7.44068e8i	−0.148549	+	0.214250i
$533$	−4.56735e8			−0.130653
$534$	1.48347e8	+	2.56944e8i	0.0421584	+	0.0730205i
$535$	−6.49414e8	+	1.12482e9i	−0.183351	+	0.317573i
$536$	−1.16068e9	+	2.01036e9i	−0.325564	+	0.563894i
$537$	8.64322e8	+	1.49705e9i	0.240860	+	0.417182i
$538$	−4.65176e9			−1.28789
$539$	5.26639e9	+	8.78487e8i	1.44861	+	0.241643i
$540$	3.89009e8			0.106312
$541$	−1.95081e9	−	3.37891e9i	−0.529695	−	0.917458i	−0.999400	−	0.0346347i	$-0.988973\pi$
$541$	−1.95081e9	−	3.37891e9i	−0.529695	−	0.917458i	0.469705	−	0.882823i	$-0.344360\pi$
$542$	9.67350e8	−	1.67550e9i	0.260967	−	0.452009i
$543$	−8.92253e7	+	1.54543e8i	−0.0239160	+	0.0414237i
$544$	−5.06584e8	−	8.77430e8i	−0.134914	−	0.233677i
$545$	3.36746e9			0.891076
$546$	1.10976e8	−	1.60060e8i	0.0291780	−	0.0420832i
$547$	1.55347e9			0.405833			0.202917	−	0.979196i	$-0.434958\pi$
$547$	1.55347e9			0.405833			0.202917	+	0.979196i	$0.434958\pi$
$548$	−1.76887e9	−	3.06378e9i	−0.459161	−	0.795291i
$549$	8.68862e8	−	1.50491e9i	0.224103	−	0.388158i
$550$	−4.47014e8	+	7.74252e8i	−0.114565	+	0.198432i
$551$	−2.70097e8	−	4.67822e8i	−0.0687842	−	0.119138i
$552$	−1.12116e9			−0.283715
$553$	6.26627e8	+	5.19052e7i	0.157569	+	0.0130519i
$554$	1.98025e9			0.494808
$555$	4.62108e7	+	8.00394e7i	0.0114741	+	0.0198737i
$556$	1.04388e9	−	1.80805e9i	0.257566	−	0.446118i
$557$	1.07718e9	−	1.86574e9i	0.264117	−	0.457464i	−0.703215	−	0.710977i	$-0.748253\pi$
$557$	1.07718e9	−	1.86574e9i	0.264117	−	0.457464i	0.967332	+	0.253513i	$0.0815861\pi$
$558$	−4.68052e8	−	8.10689e8i	−0.114044	−	0.197531i
$559$	4.53045e8			0.109698
$560$	4.89914e8	+	1.03807e9i	0.117886	+	0.249786i
$561$	5.41230e9			1.29423
$562$	1.47441e9	+	2.55375e9i	0.350380	+	0.606877i
$563$	2.15812e9	−	3.73798e9i	0.509679	−	0.882790i	−0.490258	−	0.871577i	$-0.663097\pi$
$563$	2.15812e9	−	3.73798e9i	0.509679	−	0.882790i	0.999937	−	0.0112127i	$-0.00356920\pi$
$564$	−2.59195e8	+	4.48939e8i	−0.0608345	+	0.105368i
$565$	−1.10958e9	−	1.92185e9i	−0.258815	−	0.448281i
$566$	1.32923e9			0.308136
$567$	2.05838e8	+	4.36146e8i	0.0474226	+	0.100483i
$568$	−2.05157e9			−0.469751
$569$	1.29318e9	+	2.23985e9i	0.294282	+	0.509712i	0.974818	−	0.223003i	$-0.0715860\pi$
$569$	1.29318e9	+	2.23985e9i	0.294282	+	0.509712i	−0.680535	+	0.732715i	$0.738253\pi$
$570$	5.19923e8	−	9.00532e8i	0.117592	−	0.203675i
$571$	−1.86709e9	+	3.23390e9i	−0.419701	+	0.726943i	−0.995909	−	0.0903597i	$-0.971198\pi$
$571$	−1.86709e9	+	3.23390e9i	−0.419701	+	0.726943i	0.576208	+	0.817303i	$0.304532\pi$
$572$	−2.06139e8	−	3.57042e8i	−0.0460546	−	0.0797689i
$573$	6.10658e8			0.135599
$574$	3.32575e9	+	2.75481e8i	0.734003	+	0.0607995i
$575$	−1.39801e9			−0.306671
$576$	−9.55515e7	−	1.65500e8i	−0.0208333	−	0.0360844i
$577$	2.23301e9	−	3.86770e9i	0.483923	−	0.838179i	−0.515907	−	0.856645i	$-0.672545\pi$
$577$	2.23301e9	−	3.86770e9i	0.483923	−	0.838179i	0.999829	+	0.0184657i	$0.00587815\pi$
$578$	−2.18270e9	+	3.78054e9i	−0.470160	+	0.814341i
$579$	−2.16046e8	−	3.74202e8i	−0.0462563	−	0.0801182i
$580$	−6.84845e8			−0.145745
$581$	1.37453e9	−	1.98247e9i	0.290761	−	0.419363i
$582$	6.47004e7			0.0136043
$583$	−6.15243e9	−	1.06563e10i	−1.28590	−	2.22724i
$584$	8.89114e8	−	1.53999e9i	0.184719	−	0.319943i
$585$	−1.11843e8	+	1.93718e8i	−0.0230974	+	0.0400059i
$586$	1.05966e8	+	1.83539e8i	0.0217533	+	0.0376778i
$587$	7.59680e9			1.55023			0.775117	−	0.631818i	$-0.217691\pi$
$587$	7.59680e9			1.55023			0.775117	+	0.631818i	$0.217691\pi$
$588$	−9.04623e8	+	1.09855e9i	−0.183505	+	0.222844i
$589$	−2.50226e9			−0.504579
$590$	3.65958e9	+	6.33858e9i	0.733583	+	1.27060i
$591$	1.74778e8	−	3.02725e8i	0.0348282	−	0.0603242i
$592$	2.27013e7	−	3.93198e7i	0.00449702	−	0.00778906i
$593$	−3.78292e9	−	6.55221e9i	−0.744965	−	1.29032i	−0.950211	−	0.311607i	$-0.899133\pi$
$593$	−3.78292e9	−	6.55221e9i	−0.744965	−	1.29032i	0.205246	−	0.978711i	$-0.434201\pi$
$594$	1.02086e9			0.199855
$595$	4.93712e9	−	7.12077e9i	0.960870	−	1.38585i
$596$	−4.11262e9			−0.795713
$597$	2.73796e9	+	4.74228e9i	0.526643	+	0.912173i
$598$	3.22343e8	−	5.58314e8i	0.0616401	−	0.106764i
$599$	2.56777e9	−	4.44751e9i	0.488161	−	0.845519i	−0.511747	−	0.859136i	$-0.671001\pi$
$599$	2.56777e9	−	4.44751e9i	0.488161	−	0.845519i	0.999907	+	0.0136173i	$0.00433466\pi$
$600$	−1.19146e8	−	2.06367e8i	−0.0225190	−	0.0390041i
$601$	−5.69082e9			−1.06934			−0.534668	−	0.845062i	$-0.679563\pi$
$601$	−5.69082e9			−1.06934			−0.534668	+	0.845062i	$0.679563\pi$
$602$	−3.29888e9	−	2.73256e8i	−0.616281	−	0.0510483i
$603$	3.30522e9			0.613890
$604$	−1.99210e9	−	3.45042e9i	−0.367860	−	0.637151i
$605$	−3.48091e9	+	6.02911e9i	−0.639070	+	1.10690i
$606$	−1.53318e8	+	2.65554e8i	−0.0279858	+	0.0484728i
$607$	−1.43923e9	−	2.49281e9i	−0.261197	−	0.452407i	0.705363	−	0.708846i	$-0.250784\pi$
$607$	−1.43923e9	−	2.49281e9i	−0.261197	−	0.452407i	−0.966560	+	0.256439i	$0.917451\pi$
$608$	−5.10830e8			−0.0921751
$609$	−3.62375e8	−	7.67829e8i	−0.0650126	−	0.137754i
$610$	−5.88887e9			−1.05046
$611$	−1.49041e8	−	2.58147e8i	−0.0264339	−	0.0457849i
$612$	−7.21289e8	+	1.24931e9i	−0.127198	+	0.220313i
$613$	−4.36739e9	+	7.56455e9i	−0.765792	+	1.32639i	0.174035	+	0.984739i	$0.444319\pi$
$613$	−4.36739e9	+	7.56455e9i	−0.765792	+	1.32639i	−0.939827	+	0.341651i	$0.889014\pi$
$614$	2.83903e9	+	4.91735e9i	0.494973	+	0.857318i
$615$	−3.83260e9			−0.664402
$616$	1.28566e9	+	2.72417e9i	0.221613	+	0.469571i
$617$	−2.09281e9			−0.358701			−0.179350	−	0.983785i	$-0.557400\pi$
$617$	−2.09281e9			−0.358701			−0.179350	+	0.983785i	$0.557400\pi$
$618$	−2.02161e9	−	3.50152e9i	−0.344538	−	0.596757i
$619$	−1.35754e9	+	2.35132e9i	−0.230057	+	0.398470i	−0.957825	−	0.287354i	$-0.907224\pi$
$619$	−1.35754e9	+	2.35132e9i	−0.230057	+	0.398470i	0.727768	+	0.685823i	$0.240558\pi$
$620$	−1.58615e9	+	2.74730e9i	−0.267285	+	0.462951i
$621$	7.98171e8	+	1.38247e9i	0.133744	+	0.231652i
$622$	3.38633e8			0.0564238
$623$	1.24226e9	+	1.02900e8i	0.205828	+	0.0170493i
$624$	1.09887e8			0.0181051
$625$	3.57653e9	+	6.19474e9i	0.585979	+	1.01495i
$626$	3.24039e7	−	5.61251e7i	0.00527942	−	0.00914423i
$627$	1.36441e9	−	2.36323e9i	0.221060	−	0.382887i
$628$	−5.69532e8	−	9.86458e8i	−0.0917612	−	0.158935i
$629$	−3.42730e8			−0.0549130
$630$	9.31236e8	−	1.34311e9i	0.148377	−	0.214004i
$631$	5.11357e9			0.810254			0.405127	−	0.914260i	$-0.367227\pi$
$631$	5.11357e9			0.810254			0.405127	+	0.914260i	$0.367227\pi$
$632$	1.77374e8	+	3.07221e8i	0.0279499	+	0.0484107i
$633$	−3.43688e9	+	5.95286e9i	−0.538582	+	0.932851i
$634$	1.89953e9	−	3.29008e9i	0.296029	−	0.512737i
$635$	2.50309e9	+	4.33548e9i	0.387943	+	0.671937i
$636$	3.27970e9			0.505515
$637$	−2.86969e8	−	7.66324e8i	−0.0439894	−	0.117469i
$638$	−1.79721e9			−0.273986
$639$	1.46054e9	+	2.52973e9i	0.221443	+	0.383550i
$640$	−3.23809e8	+	5.60853e8i	−0.0488269	+	0.0845706i
$641$	1.99007e9	−	3.44691e9i	0.298446	−	0.516923i	−0.677335	−	0.735675i	$-0.736865\pi$
$641$	1.99007e9	−	3.44691e9i	0.298446	−	0.516923i	0.975781	+	0.218752i	$0.0701984\pi$
$642$	−4.54241e8	−	7.86769e8i	−0.0677507	−	0.117348i
$643$	−1.15835e10			−1.71830			−0.859152	−	0.511721i	$-0.829008\pi$
$643$	−1.15835e10			−1.71830			−0.859152	+	0.511721i	$0.829008\pi$
$644$	−2.68391e9	+	3.87098e9i	−0.395975	+	0.571111i
$645$	3.80164e9			0.557843
$646$	1.92805e9	+	3.33948e9i	0.281387	+	0.487377i
$647$	3.14313e9	−	5.44406e9i	0.456244	−	0.790237i	−0.542515	−	0.840046i	$-0.682528\pi$
$647$	3.14313e9	−	5.44406e9i	0.456244	−	0.790237i	0.998759	+	0.0498088i	$0.0158612\pi$
$648$	−1.36049e8	+	2.35644e8i	−0.0196419	+	0.0340207i
$649$	9.60371e9	+	1.66341e10i	1.37906	+	2.38860i
$650$	1.37021e8			0.0195700
$651$	−3.91948e9	−	3.24661e8i	−0.556794	−	0.0461208i
$652$	2.45976e9			0.347557
$653$	−1.69599e9	−	2.93753e9i	−0.238356	−	0.412845i	0.721887	−	0.692011i	$-0.243275\pi$
$653$	−1.69599e9	−	2.93753e9i	−0.238356	−	0.412845i	−0.960243	+	0.279167i	$0.909942\pi$
$654$	−1.17771e9	+	2.03985e9i	−0.164632	+	0.285152i
$655$	−1.04295e9	+	1.80645e9i	−0.145017	+	0.251177i
$656$	9.41394e8	+	1.63054e9i	0.130199	+	0.225511i
$657$	−2.53189e9			−0.348310
$658$	9.29552e8	+	1.96961e9i	0.127199	+	0.269519i
$659$	1.04865e10			1.42735			0.713676	−	0.700476i	$-0.247029\pi$
$659$	1.04865e10			1.42735			0.713676	+	0.700476i	$0.247029\pi$
$660$	−1.72977e9	−	2.99605e9i	−0.234199	−	0.405645i
$661$	−3.12980e9	+	5.42097e9i	−0.421513	+	0.730082i	−0.996088	−	0.0883702i	$-0.971834\pi$
$661$	−3.12980e9	+	5.42097e9i	−0.421513	+	0.730082i	0.574575	+	0.818452i	$0.305167\pi$
$662$	3.64014e9	−	6.30491e9i	0.487658	−	0.844648i
$663$	−4.14752e8	−	7.18371e8i	−0.0552702	−	0.0957308i
$664$	1.36104e9			0.180419
$665$	−1.86460e9	−	3.95086e9i	−0.245872	−	0.520974i
$666$	−6.46454e7			−0.00847965
$667$	−1.40517e9	−	2.43382e9i	−0.183353	−	0.317577i
$668$	1.73642e9	−	3.00757e9i	0.225391	−	0.390389i
$669$	−2.66613e9	+	4.61787e9i	−0.344262	+	0.596280i
$670$	−5.60044e9	−	9.70025e9i	−0.719384	−	1.24601i
$671$	−1.54540e10			−1.97474
$672$	−8.00151e8	−	6.62787e7i	−0.101714	−	0.00842523i
$673$	5.20341e9			0.658014			0.329007	−	0.944327i	$-0.393286\pi$
$673$	5.20341e9			0.658014			0.329007	+	0.944327i	$0.393286\pi$
$674$	5.37689e9	+	9.31305e9i	0.676428	+	1.17161i
$675$	−1.69643e8	+	2.93831e8i	−0.0212311	+	0.0367734i
$676$	1.97636e9	−	3.42315e9i	0.246066	−	0.426200i
$677$	3.15953e9	+	5.47247e9i	0.391347	+	0.677833i	0.992628	−	0.121205i	$-0.0386758\pi$
$677$	3.15953e9	+	5.47247e9i	0.391347	+	0.677833i	−0.601280	+	0.799038i	$0.705342\pi$
$678$	1.55222e9			0.191271
$679$	1.54884e8	−	2.23388e8i	0.0189873	−	0.0273852i
$680$	4.88867e9			0.596224
$681$	−8.35685e8	−	1.44745e9i	−0.101398	−	0.175626i
$682$	−4.16249e9	+	7.20964e9i	−0.502467	+	0.870298i
$683$	3.27270e9	−	5.66848e9i	0.393037	−	0.680760i	−0.599811	−	0.800141i	$-0.704758\pi$
$683$	3.27270e9	−	5.66848e9i	0.393037	−	0.680760i	0.992849	+	0.119381i	$0.0380910\pi$
$684$	3.63667e8	+	6.29889e8i	0.0434517	+	0.0752606i
$685$	1.70701e10			2.02917
$686$	1.62738e9	+	5.75314e9i	0.192466	+	0.680409i
$687$	−8.38096e9			−0.986155
$688$	−9.33788e8	−	1.61737e9i	−0.109317	−	0.189343i
$689$	−9.42937e8	+	1.63322e9i	−0.109829	+	0.190229i
$690$	2.70488e9	−	4.68498e9i	0.313455	−	0.542921i
$691$	1.35415e9	+	2.34545e9i	0.156132	+	0.270429i	0.933471	−	0.358653i	$-0.116764\pi$
$691$	1.35415e9	+	2.34545e9i	0.156132	+	0.270429i	−0.777338	+	0.629083i	$0.783431\pi$
$692$	1.09508e9			0.125624
$693$	2.44381e9	−	3.52469e9i	0.278934	−	0.402304i
$694$	−3.81460e9			−0.433203
$695$	5.03686e9	+	8.72409e9i	0.569132	+	0.985765i
$696$	2.39512e8	−	4.14847e8i	0.0269274	−	0.0466397i
$697$	7.10629e9	−	1.23085e10i	0.794929	−	1.37686i
$698$	−3.86916e9	−	6.70159e9i	−0.430649	−	0.745905i
$699$	3.33480e9			0.369317
$700$	−9.97731e8	−	8.26448e7i	−0.109944	−	0.00910694i
$701$	−8.01526e9			−0.878830			−0.439415	−	0.898284i	$-0.644814\pi$
$701$	−8.01526e9			−0.878830			−0.439415	+	0.898284i	$0.644814\pi$
$702$	−7.82301e7	−	1.35499e8i	−0.00853482	−	0.0147827i
$703$	−8.64005e7	+	1.49650e8i	−0.00937935	+	0.0162455i
$704$	−8.49760e8	+	1.47183e9i	−0.0917893	+	0.158984i
$705$	−1.25065e9	−	2.16619e9i	−0.134423	−	0.232828i
$706$	5.46372e9			0.584349
$707$	5.49843e8	+	1.16505e9i	0.0585155	+	0.123987i
$708$	−5.11949e9			−0.542138
$709$	6.99354e9	+	1.21132e10i	0.736945	+	1.27643i	0.953865	+	0.300237i	$0.0970658\pi$
$709$	6.99354e9	+	1.21132e10i	0.736945	+	1.27643i	−0.216919	+	0.976190i	$0.569601\pi$
$710$	4.94955e9	−	8.57287e9i	0.518993	−	0.898922i
$711$	2.52550e8	−	4.37430e8i	0.0263514	−	0.0456420i
$712$	3.51637e8	+	6.09053e8i	0.0365102	+	0.0632376i
$713$	−1.30179e10			−1.34502
$714$	2.58676e9	+	5.48104e9i	0.265958	+	0.563532i
$715$	1.98929e9			0.203529
$716$	2.04876e9	+	3.54856e9i	0.208591	+	0.361291i
$717$	−2.52140e9	+	4.36720e9i	−0.255461	+	0.442472i
$718$	4.50720e9	−	7.80670e9i	0.454435	−	0.787104i
$719$	−9.24603e9	−	1.60146e10i	−0.927693	−	1.60681i	−0.787172	−	0.616733i	$-0.788456\pi$
$719$	−9.24603e9	−	1.60146e10i	−0.927693	−	1.60681i	−0.140520	−	0.990078i	$-0.544878\pi$
$720$	9.22096e8			0.0920688
$721$	−1.69290e10	−	1.40228e9i	−1.68212	−	0.139335i
$722$	−5.20677e9			−0.514859
$723$	1.47575e9	+	2.55608e9i	0.145221	+	0.251530i
$724$	−2.11497e8	+	3.66324e8i	−0.0207119	+	0.0358740i
$725$	2.98654e8	−	5.17284e8i	0.0291062	−	0.0504134i
$726$	−2.43477e9	−	4.21714e9i	−0.236145	−	0.409016i
$727$	−6.52913e8			−0.0630210			−0.0315105	−	0.999503i	$-0.510032\pi$
$727$	−6.52913e8			−0.0630210			−0.0315105	+	0.999503i	$0.510032\pi$
$728$	2.63055e8	−	3.79402e8i	0.0252689	−	0.0364451i
$729$	3.87420e8			0.0370370
$730$	4.29009e9	+	7.43065e9i	0.408165	+	0.706963i
$731$	−7.04888e9	+	1.22090e10i	−0.667436	+	1.15603i
$732$	2.05952e9	−	3.56720e9i	0.194079	−	0.336154i
$733$	2.99898e9	+	5.19439e9i	0.281261	+	0.487159i	0.971696	−	0.236236i	$-0.0759140\pi$
$733$	2.99898e9	+	5.19439e9i	0.281261	+	0.487159i	−0.690434	+	0.723395i	$0.742581\pi$
$734$	−8.19443e9			−0.764861
$735$	−2.40805e9	−	6.43046e9i	−0.223697	−	0.597361i
$736$	−2.65757e9			−0.245704
$737$	−1.46970e10	−	2.54560e10i	−1.35236	−	2.34236i
$738$	1.34038e9	−	2.32161e9i	0.122753	−	0.212614i
$739$	−1.54303e9	+	2.67261e9i	−0.140644	+	0.243602i	−0.927739	−	0.373229i	$-0.878250\pi$
$739$	−1.54303e9	+	2.67261e9i	−0.140644	+	0.243602i	0.787096	+	0.616831i	$0.211584\pi$
$740$	1.09537e8	+	1.89723e8i	0.00993684	+	0.0172111i
$741$	−4.18228e8			−0.0377615
$742$	7.85115e9	−	1.13236e10i	0.705537	−	1.01759i
$743$	−1.65397e10			−1.47933			−0.739667	−	0.672974i	$-0.765017\pi$
$743$	−1.65397e10			−1.47933			−0.739667	+	0.672974i	$0.765017\pi$
$744$	−1.10946e9	−	1.92163e9i	−0.0987654	−	0.171067i
$745$	9.92195e9	−	1.71853e10i	0.879124	−	1.52269i
$746$	2.80466e9	−	4.85781e9i	0.247340	−	0.428405i
$747$	−9.68941e8	−	1.67825e9i	−0.0850502	−	0.147311i
$748$	1.28292e10			1.12084
$749$	−3.80383e9	−	3.15082e8i	−0.330777	−	0.0273991i
$750$	−4.06135e9			−0.351525
$751$	9.01861e8	+	1.56207e9i	0.0776962	+	0.134574i	0.902256	−	0.431202i	$-0.141910\pi$
$751$	9.01861e8	+	1.56207e9i	0.0776962	+	0.134574i	−0.824559	+	0.565775i	$0.808577\pi$
$752$	−6.14389e8	+	1.06415e9i	−0.0526842	+	0.0912518i
$753$	1.78525e9	−	3.09214e9i	0.152376	−	0.263923i
$754$	1.37723e8	+	2.38543e8i	0.0117006	+	0.0202660i
$755$	1.92243e10			1.62568
$756$	4.87912e8	+	1.03383e9i	0.0410691	+	0.0870206i
$757$	−8.71019e9			−0.729780			−0.364890	−	0.931051i	$-0.618893\pi$
$757$	−8.71019e9			−0.729780			−0.364890	+	0.931051i	$0.618893\pi$
$758$	−1.36014e9	−	2.35583e9i	−0.113433	−	0.196472i
$759$	7.09831e9	−	1.22946e10i	0.589263	−	1.02063i
$760$	1.23241e9	−	2.13460e9i	0.101837	−	0.176388i
$761$	1.14245e10	+	1.97879e10i	0.939707	+	1.62762i	0.766017	+	0.642820i	$0.222236\pi$
$761$	1.14245e10	+	1.97879e10i	0.939707	+	1.62762i	0.173690	+	0.984800i	$0.444431\pi$
$762$	−3.50164e9			−0.286701
$763$	4.22361e9	+	8.94933e9i	0.344230	+	0.729382i
$764$	1.44749e9			0.117432
$765$	−3.48031e9	−	6.02808e9i	−0.281063	−	0.486815i
$766$	3.43971e9	−	5.95775e9i	0.276516	−	0.478941i
$767$	1.47189e9	−	2.54939e9i	0.117785	−	0.204010i
$768$	−2.26492e8	−	3.92296e8i	−0.0180422	−	0.0312500i
$769$	−1.04328e10			−0.827288			−0.413644	−	0.910439i	$-0.635744\pi$
$769$	−1.04328e10			−0.827288			−0.413644	+	0.910439i	$0.635744\pi$
$770$	−1.44852e10	−	1.19985e9i	−1.14342	−	0.0947127i
$771$	−3.36010e9			−0.264036
$772$	−5.12108e8	−	8.86998e8i	−0.0400591	−	0.0693844i
$773$	−9.22414e9	+	1.59767e10i	−0.718286	+	1.24411i	0.243392	+	0.969928i	$0.421740\pi$
$773$	−9.22414e9	+	1.59767e10i	−0.718286	+	1.24411i	−0.961678	+	0.274180i	$0.911593\pi$
$774$	−1.32955e9	+	2.30286e9i	−0.103065	+	0.178514i
$775$	−1.38341e9	−	2.39614e9i	−0.106757	−	0.184908i
$776$	1.53364e8			0.0117817
$777$	−1.54752e8	+	2.23198e8i	−0.0118349	+	0.0170694i
$778$	1.54440e8			0.0117579
$779$	−3.58292e9	−	6.20580e9i	−0.271554	−	0.470345i
$780$	−2.65110e8	+	4.59183e8i	−0.0200030	+	0.0346461i
$781$	1.29889e10	−	2.24975e10i	0.975651	−	1.68988i
$782$	1.00306e10	+	1.73735e10i	0.750072	+	1.29916i
$783$	−6.82048e8			−0.0507749
$784$	−2.14429e9	+	2.60398e9i	−0.158920	+	0.192989i
$785$	5.49613e9			0.405521
$786$	−7.29506e8	−	1.26354e9i	−0.0535859	−	0.0928134i
$787$	−8.74207e9	+	1.51417e10i	−0.639297	+	1.10730i	0.346290	+	0.938128i	$0.387441\pi$
$787$	−8.74207e9	+	1.51417e10i	−0.639297	+	1.10730i	−0.985587	+	0.169168i	$0.945892\pi$
$788$	4.14289e8	−	7.17570e8i	0.0301621	−	0.0522423i
$789$	6.56426e9	+	1.13696e10i	0.475791	+	0.824095i
$790$	−1.71171e9			−0.123519
$791$	3.71581e9	−	5.35928e9i	0.266954	−	0.385025i
$792$	2.41982e9			0.173080
$793$	1.18426e9	+	2.05119e9i	0.0843315	+	0.146066i
$794$	2.61344e9	−	4.52662e9i	0.185285	−	0.320924i
$795$	−7.91248e9	+	1.37048e10i	−0.558506	+	0.967361i
$796$	6.48997e9	+	1.12410e10i	0.456086	+	0.789965i
$797$	8.77363e9			0.613869			0.306934	−	0.951731i	$-0.400697\pi$
$797$	8.77363e9			0.613869			0.306934	+	0.951731i	$0.400697\pi$
$798$	3.04536e9	+	2.52255e8i	0.212143	+	0.0175724i
$799$	9.27567e9			0.643326
$800$	−2.82420e8	−	4.89165e8i	−0.0195020	−	0.0337785i
$801$	5.00671e8	−	8.67187e8i	0.0344222	−	0.0596210i
$802$	−6.92421e9	+	1.19931e10i	−0.473980	+	0.820958i
$803$	1.12583e10	+	1.95000e10i	0.767307	+	1.32902i
$804$	7.83461e9			0.531644
$805$	−9.70051e9	−	2.05542e10i	−0.655404	−	1.38872i
$806$	1.27591e9			0.0858315
$807$	7.84984e9	+	1.35963e10i	0.525779	+	0.910676i
$808$	−3.63419e8	+	6.29461e8i	−0.0242364	+	0.0419787i
$809$	1.23018e10	−	2.13073e10i	0.816862	−	1.41485i	−0.0911204	−	0.995840i	$-0.529045\pi$
$809$	1.23018e10	−	2.13073e10i	0.816862	−	1.41485i	0.907983	−	0.419007i	$-0.137622\pi$
$810$	−6.56453e8	−	1.13701e9i	−0.0434017	−	0.0751739i
$811$	2.27226e10			1.49584			0.747921	−	0.663788i	$-0.231052\pi$
$811$	2.27226e10			1.49584			0.747921	+	0.663788i	$0.231052\pi$
$812$	−8.58962e8	−	1.82004e9i	−0.0563025	−	0.119298i
$813$	−6.52961e9			−0.426158
$814$	2.87453e8	+	4.97883e8i	0.0186802	+	0.0323550i
$815$	−5.93433e9	+	1.02786e10i	−0.383990	+	0.665090i
$816$	−1.70972e9	+	2.96133e9i	−0.110156	+	0.190797i
$817$	3.55398e9	+	6.15567e9i	0.228001	+	0.394910i
$818$	−1.43738e10			−0.918196
$819$	−6.55102e8	−	5.42639e7i	−0.0416692	−	0.00345157i
$820$	−9.08469e9			−0.575389
$821$	−6.78361e9	−	1.17496e10i	−0.427819	−	0.741004i	0.568860	−	0.822434i	$-0.307384\pi$
$821$	−6.78361e9	−	1.17496e10i	−0.427819	−	0.741004i	−0.996679	+	0.0814306i	$0.974051\pi$
$822$	−5.96995e9	+	1.03403e10i	−0.374904	+	0.649352i
$823$	−1.20715e10	+	2.09085e10i	−0.754854	+	1.30744i	0.190593	+	0.981669i	$0.438959\pi$
$823$	−1.20715e10	+	2.09085e10i	−0.754854	+	1.30744i	−0.945447	+	0.325776i	$0.894375\pi$
$824$	−4.79195e9	−	8.29991e9i	−0.298378	−	0.516807i
$825$	3.01735e9			0.187084
$826$	−1.22554e10	+	1.76758e10i	−0.756651	+	1.09131i
$827$	5.22827e9			0.321432			0.160716	−	0.987001i	$-0.448620\pi$
$827$	5.22827e9			0.321432			0.160716	+	0.987001i	$0.448620\pi$
$828$	1.89196e9	+	3.27697e9i	0.115826	+	0.200617i
$829$	4.00404e9	−	6.93520e9i	0.244094	−	0.422784i	−0.717782	−	0.696268i	$-0.754843\pi$
$829$	4.00404e9	−	6.93520e9i	0.244094	−	0.422784i	0.961877	+	0.273484i	$0.0881761\pi$
$830$	−3.28359e9	+	5.68734e9i	−0.199331	+	0.345252i
$831$	−3.34168e9	−	5.78795e9i	−0.202004	−	0.349882i
$832$	2.60473e8			0.0156795
$833$	2.51165e10	+	4.18968e9i	1.50557	+	0.251144i
$834$	−7.04619e9			−0.420604
$835$	8.37845e9	+	1.45119e10i	0.498036	+	0.862624i
$836$	3.23417e9	−	5.60174e9i	0.191443	−	0.331590i
$837$	−1.57967e9	+	2.73608e9i	−0.0931169	+	0.161283i
$838$	−4.74931e9	−	8.22605e9i	−0.278790	−	0.482878i
$839$	1.13828e10			0.665397			0.332699	−	0.943033i	$-0.392041\pi$
$839$	1.13828e10			0.665397			0.332699	+	0.943033i	$0.392041\pi$
$840$	2.20737e9	−	3.18368e9i	0.128499	−	0.185332i
$841$	−1.60491e10			−0.930392
$842$	1.46574e9	+	2.53874e9i	0.0846185	+	0.146563i
$843$	4.97612e9	−	8.61889e9i	0.286084	−	0.495513i
$844$	−8.14669e9	+	1.41105e10i	−0.466426	+	0.807873i
$845$	9.53619e9	+	1.65172e10i	0.543721	+	0.941753i
$846$	1.74957e9			0.0993424
$847$	−2.03888e10	−	1.68886e9i	−1.15292	−	0.0954997i
$848$	7.77410e9			0.437789
$849$	−2.24308e9	−	3.88512e9i	−0.125796	−	0.217885i
$850$	−2.13190e9	+	3.69256e9i	−0.119070	+	0.206234i
$851$	−4.49495e8	+	7.78549e8i	−0.0250018	+	0.0433044i
$852$	3.46203e9	+	5.99641e9i	0.191775	+	0.332164i
$853$	2.07865e9			0.114673			0.0573364	−	0.998355i	$-0.481739\pi$
$853$	2.07865e9			0.114673			0.0573364	+	0.998355i	$0.481739\pi$
$854$	−7.38608e9	−	1.56502e10i	−0.405799	−	0.859840i
$855$	−3.50948e9			−0.192026
$856$	−1.07672e9	−	1.86493e9i	−0.0586738	−	0.101626i
$857$	−5.94941e9	+	1.03047e10i	−0.322880	+	0.559244i	−0.981081	−	0.193598i	$-0.937984\pi$
$857$	−5.94941e9	+	1.03047e10i	−0.322880	+	0.559244i	0.658201	+	0.752842i	$0.271318\pi$
$858$	−6.95718e8	+	1.20502e9i	−0.0376034	+	0.0651311i
$859$	−1.27030e10	−	2.20023e10i	−0.683803	−	1.18438i	−0.973811	−	0.227357i	$-0.926991\pi$
$859$	−1.27030e10	−	2.20023e10i	−0.683803	−	1.18438i	0.290009	−	0.957024i	$-0.406342\pi$
$860$	9.01130e9			0.483106
$861$	−4.80702e9	−	1.01855e10i	−0.256664	−	0.543840i
$862$	−5.22753e8			−0.0277985
$863$	−2.99783e9	−	5.19239e9i	−0.158770	−	0.274998i	0.775655	−	0.631157i	$-0.217420\pi$
$863$	−2.99783e9	−	5.19239e9i	−0.158770	−	0.274998i	−0.934425	+	0.356159i	$0.884086\pi$
$864$	−3.22486e8	+	5.58563e8i	−0.0170103	+	0.0294628i
$865$	−2.64195e9	+	4.57599e9i	−0.138793	+	0.240397i
$866$	6.22254e9	+	1.07778e10i	0.325578	+	0.563918i
$867$	1.47332e10			0.767768
$868$	−9.29062e9	−	7.69568e8i	−0.482198	−	0.0399418i
$869$	−4.49197e9			−0.232203
$870$	1.15568e9	+	2.00169e9i	0.0595002	+	0.103057i
$871$	−2.25251e9	+	3.90146e9i	−0.115506	+	0.200061i
$872$	−2.79160e9	+	4.83520e9i	−0.142576	+	0.246949i
$873$	−1.09182e8	−	1.89109e8i	−0.00555394	−	0.00961970i
$874$	1.01147e10			0.512461
$875$	−9.72232e9	+	1.40224e10i	−0.490616	+	0.707612i
$876$	−6.00152e9			−0.301645
$877$	4.41384e9	+	7.64499e9i	0.220962	+	0.382718i	0.955100	−	0.296282i	$-0.0957470\pi$
$877$	4.41384e9	+	7.64499e9i	0.220962	+	0.382718i	−0.734138	+	0.679000i	$0.762414\pi$
$878$	1.06904e10	−	1.85163e10i	0.533044	−	0.923260i
$879$	3.57636e8	−	6.19443e8i	0.0177615	−	0.0307638i
$880$	−4.10020e9	−	7.10176e9i	−0.202822	−	0.351299i
$881$	7.07937e9			0.348802			0.174401	−	0.984675i	$-0.444201\pi$
$881$	7.07937e9			0.348802			0.174401	+	0.984675i	$0.444201\pi$
$882$	4.73744e9	+	7.90253e8i	0.232490	+	0.0387817i
$883$	3.43253e10			1.67785			0.838923	−	0.544251i	$-0.183186\pi$
$883$	3.43253e10			1.67785			0.838923	+	0.544251i	$0.183186\pi$
$884$	−9.83116e8	−	1.70281e9i	−0.0478654	−	0.0829053i
$885$	1.23511e10	−	2.13927e10i	0.598968	−	1.03744i
$886$	9.38537e9	−	1.62559e10i	0.453350	−	0.785225i
$887$	−5.23222e9	−	9.06247e9i	−0.251741	−	0.436028i	0.712264	−	0.701911i	$-0.247670\pi$
$887$	−5.23222e9	−	9.06247e9i	−0.251741	−	0.436028i	−0.964005	+	0.265884i	$0.914336\pi$
$888$	−1.53234e8			−0.00734360
$889$	−8.38244e9	+	1.20899e10i	−0.400142	+	0.577122i
$890$	−3.39339e9			−0.161350
$891$	−1.72271e9	−	2.98382e9i	−0.0815905	−	0.141319i
$892$	−6.31971e9	+	1.09461e10i	−0.298140	+	0.516393i
$893$	2.33835e9	−	4.05014e9i	0.109883	−	0.190322i
$894$	6.94004e9	+	1.20205e10i	0.324848	+	0.562654i
$895$	−1.97711e10			−0.921828
$896$	−1.89665e9	−	1.57105e8i	−0.0880867	−	0.00729646i
$897$	−2.17581e9			−0.100658
$898$	−8.30334e9	−	1.43818e10i	−0.382636	−	0.662745i
$899$	2.78099e9	−	4.81682e9i	0.127656	−	0.221107i
$900$	−4.02117e8	+	6.96487e8i	−0.0183867	+	0.0318467i
$901$	−2.93421e10	−	5.08221e10i	−1.33646	−	2.31481i
$902$	−2.38406e10			−1.08167
$903$	4.76818e9	+	1.01032e10i	0.215499	+	0.456617i
$904$	3.67934e9			0.165646
$905$	−1.02050e9	−	1.76756e9i	−0.0457660	−	0.0792691i
$906$	−6.72334e9	+	1.16452e10i	−0.300356	+	0.520232i
$907$	1.54783e10	−	2.68092e10i	0.688806	−	1.19305i	−0.283418	−	0.958996i	$-0.591468\pi$
$907$	1.54783e10	−	2.68092e10i	0.688806	−	1.19305i	0.972224	−	0.234051i	$-0.0751983\pi$
$908$	−1.98088e9	−	3.43099e9i	−0.0878129	−	0.152096i
$909$	1.03489e9			0.0457006
$910$	9.50763e8	+	2.01455e9i	0.0418242	+	0.0886204i
$911$	1.55078e10			0.679572			0.339786	−	0.940503i	$-0.389645\pi$
$911$	1.55078e10			0.679572			0.339786	+	0.940503i	$0.389645\pi$
$912$	8.62025e8	+	1.49307e9i	0.0376303	+	0.0651776i
$913$	−8.61700e9	+	1.49251e10i	−0.374721	+	0.649036i
$914$	6.68058e9	−	1.15711e10i	0.289403	−	0.501260i
$915$	9.93747e9	+	1.72122e10i	0.428847	+	0.742784i
$916$	−1.98660e10			−0.854035
$917$	−6.10891e9	−	5.06018e8i	−0.261620	−	0.0216707i
$918$	4.86870e9			0.207713
$919$	−1.66116e10	−	2.87721e10i	−0.706003	−	1.22283i	−0.966328	−	0.257312i	$-0.917163\pi$
$919$	−1.66116e10	−	2.87721e10i	−0.706003	−	1.22283i	0.260325	−	0.965521i	$-0.416170\pi$
$920$	6.41156e9	−	1.11051e10i	0.271460	−	0.470183i
$921$	9.58174e9	−	1.65961e10i	0.404144	−	0.699997i
$922$	7.21094e8	+	1.24897e9i	0.0302994	+	0.0524800i
$923$	−3.98143e9			−0.166661
$924$	5.79273e9	−	8.35481e9i	0.241564	−	0.348405i
$925$	−1.91071e8			−0.00793779
$926$	1.10473e10	+	1.91346e10i	0.457214	+	0.791918i
$927$	−6.82292e9	+	1.18176e10i	−0.281314	+	0.487250i
$928$	5.67732e8	−	9.83341e8i	0.0233198	−	0.0403911i
$929$	−1.77847e8	−	3.08039e8i	−0.00727764	−	0.0126052i	0.862364	−	0.506289i	$-0.168983\pi$
$929$	−1.77847e8	−	3.08039e8i	−0.00727764	−	0.0126052i	−0.869641	+	0.493684i	$0.835650\pi$
$930$	1.07065e10			0.436474
$931$	8.16112e9	−	9.91069e9i	0.331456	−	0.402513i
$932$	7.90471e9			0.319838
$933$	−5.71443e8	−	9.89768e8i	−0.0230349	−	0.0398977i
$934$	−9.80530e9	+	1.69833e10i	−0.393774	+	0.682036i
$935$	−3.09512e10	+	5.36090e10i	−1.23833	+	2.14485i
$936$	−1.85434e8	−	3.21182e8i	−0.00739137	−	0.0128022i
$937$	4.28321e9			0.170091			0.0850454	−	0.996377i	$-0.472896\pi$
$937$	4.28321e9			0.170091			0.0850454	+	0.996377i	$0.472896\pi$
$938$	1.87550e10	−	2.70502e10i	0.742005	−	1.07019i
$939$	−2.18726e8			−0.00862126
$940$	−2.96450e9	−	5.13467e9i	−0.116414	−	0.201635i
$941$	1.65059e10	−	2.85890e10i	0.645765	−	1.11850i	−0.338359	−	0.941017i	$-0.609872\pi$
$941$	1.65059e10	−	2.85890e10i	0.645765	−	1.11850i	0.984124	−	0.177481i	$-0.0567950\pi$
$942$	−1.92217e9	+	3.32930e9i	−0.0749227	+	0.129770i
$943$	−1.86400e10	−	3.22854e10i	−0.723861	−	1.25376i
$944$	−1.21351e10			−0.469505
$945$	−5.49716e9	−	4.55345e8i	−0.211898	−	0.0175521i
$946$	2.36480e10			0.908188
$947$	−3.68911e9	−	6.38973e9i	−0.141155	−	0.244488i	0.786777	−	0.617238i	$-0.211748\pi$
$947$	−3.68911e9	−	6.38973e9i	−0.141155	−	0.244488i	−0.927932	+	0.372750i	$0.878415\pi$
$948$	5.98638e8	−	1.03687e9i	0.0228210	−	0.0395272i
$949$	1.72548e9	−	2.98862e9i	0.0655358	−	0.113511i
$950$	1.07488e9	+	1.86175e9i	0.0406751	+	0.0704513i
$951$	−1.28218e10			−0.483413
$952$	6.13158e9	+	1.29921e10i	0.230326	+	0.488033i
$953$	−6.89038e9			−0.257880			−0.128940	−	0.991652i	$-0.541158\pi$
$953$	−6.89038e9			−0.257880			−0.128940	+	0.991652i	$0.541158\pi$
$954$	−5.53449e9	−	9.58602e9i	−0.206376	−	0.357453i
$955$	−3.49215e9	+	6.04859e9i	−0.129742	+	0.224720i
$956$	−5.97666e9	+	1.03519e10i	−0.221236	+	0.383192i
$957$	3.03280e9	+	5.25296e9i	0.111854	+	0.193737i
$958$	2.74485e10			1.00865
$959$	2.14101e10	+	4.53653e10i	0.783886	+	1.66096i
$960$	2.18571e9			0.0797339
$961$	8.74329e8	+	1.51438e9i	0.0317792	+	0.0550432i
$962$	4.40558e7	−	7.63069e7i	0.00159548	−	0.00276345i
$963$	−1.53306e9	+	2.65534e9i	−0.0553182	+	0.0958140i
$964$	3.49808e9	+	6.05885e9i	0.125765	+	0.217831i
$965$	4.94198e9			0.177033
$966$	1.58433e10	+	1.31235e9i	0.565493	+	0.0468413i
$967$	2.74855e10			0.977489			0.488744	−	0.872427i	$-0.337455\pi$
$967$	2.74855e10			0.977489			0.488744	+	0.872427i	$0.337455\pi$
$968$	−5.77130e9	−	9.99618e9i	−0.204508	−	0.354218i
$969$	6.50716e9	−	1.12707e10i	0.229752	−	0.397941i
$970$	−3.70001e8	+	6.40860e8i	−0.0130167	+	0.0225456i
$971$	−2.81796e9	−	4.88085e9i	−0.0987797	−	0.171091i	0.812400	−	0.583100i	$-0.198161\pi$
$971$	−2.81796e9	−	4.88085e9i	−0.0987797	−	0.171091i	−0.911180	+	0.412009i	$0.864827\pi$
$972$	9.18330e8			0.0320750
$973$	−1.68676e10	+	2.43280e10i	−0.587028	+	0.846666i
$974$	1.51951e10			0.526923
$975$	−2.31223e8	−	4.00491e8i	−0.00798942	−	0.0138381i
$976$	4.88184e9	−	8.45559e9i	0.168077	−	0.291118i
$977$	1.54612e10	−	2.67796e10i	0.530411	−	0.918699i	−0.468959	−	0.883220i	$-0.655371\pi$
$977$	1.54612e10	−	2.67796e10i	0.530411	−	0.918699i	0.999370	−	0.0354794i	$-0.0112958\pi$
$978$	−4.15084e9	−	7.18947e9i	−0.141890	−	0.245760i
$979$	−8.90515e9			−0.303320
$980$	−5.70797e9	−	1.52426e10i	−0.193727	−	0.517330i
$981$	7.94953e9			0.268844
$982$	−2.08783e10	−	3.61622e10i	−0.703565	−	1.21861i
$983$	5.51561e9	−	9.55332e9i	0.185207	−	0.320787i	−0.758440	−	0.651743i	$-0.774038\pi$
$983$	5.51561e9	−	9.55332e9i	0.185207	−	0.320787i	0.943646	+	0.330956i	$0.107371\pi$
$984$	3.17720e9	−	5.50308e9i	0.106307	−	0.184129i
$985$	1.99900e9	+	3.46237e9i	0.0666478	+	0.115437i
$986$	−8.57127e9			−0.284758
$987$	4.18823e9	−	6.04065e9i	0.138650	−	0.199974i
$988$	−9.91354e8			−0.0327024
$989$	1.84894e10	+	3.20246e10i	0.607766	+	1.05268i
$990$	−5.83798e9	+	1.01117e10i	−0.191223	+	0.331208i
$991$	−1.80670e10	+	3.12929e10i	−0.589695	+	1.02138i	0.404578	+	0.914504i	$0.367419\pi$
$991$	−1.80670e10	+	3.12929e10i	−0.589695	+	1.02138i	−0.994272	+	0.106877i	$0.965915\pi$
$992$	−2.62982e9	−	4.55498e9i	−0.0855333	−	0.148148i
$993$	−2.45710e10			−0.796342
$994$	2.89911e10	+	2.40141e9i	0.936295	+	0.0775559i
$995$	−6.26299e10			−2.01558
$996$	−2.29675e9	−	3.97809e9i	−0.0736556	−	0.127575i
$997$	−1.16908e9	+	2.02490e9i	−0.0373603	+	0.0647099i	−0.884101	−	0.467296i	$-0.845228\pi$
$997$	−1.16908e9	+	2.02490e9i	−0.0373603	+	0.0647099i	0.846741	+	0.532006i	$0.178562\pi$
$998$	−6.87263e9	+	1.19037e10i	−0.218860	+	0.379076i
$999$	1.09089e8	+	1.88948e8i	0.00346180	+	0.00599602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.8.e.d.25.1	✓	6
3.2	odd	2		126.8.g.k.109.3		6
7.2	even	3	inner	42.8.e.d.37.1	yes	6
7.3	odd	6		294.8.a.x.1.1		3
7.4	even	3		294.8.a.y.1.3		3
7.5	odd	6		294.8.e.z.79.3		6
7.6	odd	2		294.8.e.z.67.3		6
21.2	odd	6		126.8.g.k.37.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.d.25.1	✓	6	1.1	even	1	trivial
42.8.e.d.37.1	yes	6	7.2	even	3	inner
126.8.g.k.37.3		6	21.2	odd	6
126.8.g.k.109.3		6	3.2	odd	2
294.8.a.x.1.1		3	7.3	odd	6
294.8.a.y.1.3		3	7.4	even	3
294.8.e.z.67.3		6	7.6	odd	2
294.8.e.z.79.3		6	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	42.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-154.404 - 267.436i) q^{5} +216.000 q^{6} +(517.075 - 745.773i) q^{7} +512.000 q^{8} +(-364.500 - 631.333i) q^{9} +O(q^{10})\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-154.404 - 267.436i) q^{5} +216.000 q^{6} +(517.075 - 745.773i) q^{7} +512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(-1235.23 + 2139.49i) q^{10} +(-3241.58 + 5614.58i) q^{11} +(-864.000 - 1496.49i) q^{12} +993.626 q^{13} +(-7235.16 - 599.309i) q^{14} +8337.82 q^{15} +(-2048.00 - 3547.24i) q^{16} +(-15459.7 + 26777.0i) q^{17} +(-2916.00 + 5050.66i) q^{18} +(7794.64 + 13500.7i) q^{19} +19763.7 q^{20} +(10457.7 + 22158.5i) q^{21} +51865.2 q^{22} +(40551.3 + 70236.9i) q^{23} +(-6912.00 + 11971.9i) q^{24} +(-8618.77 + 14928.1i) q^{25} +(-3974.50 - 6884.04i) q^{26} +19683.0 q^{27} +(24788.5 + 52523.9i) q^{28} -34651.6 q^{29} +(-33351.3 - 57766.1i) q^{30} +(-80255.8 + 139007. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-87522.6 - 151594. i) q^{33} +247356. q^{34} +(-279285. - 23133.9i) q^{35} +46656.0 q^{36} +(5542.31 + 9599.55i) q^{37} +(62357.1 - 108006. i) q^{38} +(-13413.9 + 23233.6i) q^{39} +(-79054.9 - 136927. i) q^{40} -459665. q^{41} +(111688. - 161087. i) q^{42} +455951. q^{43} +(-207461. - 359333. i) q^{44} +(-112561. + 194961. i) q^{45} +(324410. - 561895. i) q^{46} +(-149997. - 259803. i) q^{47} +110592. q^{48} +(-288810. - 771240. i) q^{49} +137900. q^{50} +(-417413. - 722980. i) q^{51} +(-31796.0 + 55072.3i) q^{52} +(-948986. + 1.64369e6i) q^{53} +(-78732.0 - 136368. i) q^{54} +2.00205e6 q^{55} +(264742. - 381836. i) q^{56} -420911. q^{57} +(138606. + 240073. i) q^{58} +(1.48133e6 - 2.56574e6i) q^{59} +(-266810. + 462129. i) q^{60} +(1.19185e6 + 2.06435e6i) q^{61} +1.28409e6 q^{62} +(-659304. - 54612.0i) q^{63} +262144. q^{64} +(-153420. - 265731. i) q^{65} +(-700181. + 1.21275e6i) q^{66} +(-2.26696e6 + 3.92649e6i) q^{67} +(-989423. - 1.71373e6i) q^{68} -2.18977e6 q^{69} +(956862. + 2.02748e6i) q^{70} -4.00697e6 q^{71} +(-186624. - 323242. i) q^{72} +(1.73655e6 - 3.00779e6i) q^{73} +(44338.4 - 76796.4i) q^{74} +(-232707. - 403060. i) q^{75} -997714. q^{76} +(2.51106e6 + 5.32064e6i) q^{77} +214623. q^{78} +(346434. + 600041. i) q^{79} +(-632439. + 1.09542e6i) q^{80} +(-265720. + 460241. i) q^{81} +(1.83866e6 + 3.18465e6i) q^{82} +2.65827e6 q^{83} +(-1.56280e6 - 129451. i) q^{84} +9.54818e6 q^{85} +(-1.82381e6 - 3.15892e6i) q^{86} +(467797. - 810248. i) q^{87} +(-1.65969e6 + 2.87466e6i) q^{88} +(686791. + 1.18956e6i) q^{89} +1.80097e6 q^{90} +(513779. - 741019. i) q^{91} -5.19057e6 q^{92} +(-2.16691e6 - 3.75319e6i) q^{93} +(-1.19998e6 + 2.07842e6i) q^{94} +(2.40705e6 - 4.16913e6i) q^{95} +(-442368. - 766204. i) q^{96} +299539. q^{97} +(-4.18807e6 + 5.08590e6i) q^{98} +4.72622e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 81 q^{3} - 192 q^{4} + 70 q^{5} + 1296 q^{6} - 895 q^{7} + 3072 q^{8} - 2187 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 - 81 * q^3 - 192 * q^4 + 70 * q^5 + 1296 * q^6 - 895 * q^7 + 3072 * q^8 - 2187 * q^9	\( 6 q - 24 q^{2} - 81 q^{3} - 192 q^{4} + 70 q^{5} + 1296 q^{6} - 895 q^{7} + 3072 q^{8} - 2187 q^{9} + 560 q^{10} - 2428 q^{11} - 5184 q^{12} - 3838 q^{13} - 3272 q^{14} - 3780 q^{15} - 12288 q^{16} - 24508 q^{17} - 17496 q^{18} + 1353 q^{19} - 8960 q^{20} + 35208 q^{21} + 38848 q^{22} - 96628 q^{23} - 41472 q^{24} - 135175 q^{25} + 15352 q^{26} + 118098 q^{27} + 83456 q^{28} - 228224 q^{29} + 15120 q^{30} - 221395 q^{31} - 98304 q^{32} - 65556 q^{33} + 392128 q^{34} - 136510 q^{35} + 279936 q^{36} - 249987 q^{37} + 10824 q^{38} + 51813 q^{39} + 35840 q^{40} + 1221852 q^{41} - 193320 q^{42} + 1200486 q^{43} - 155392 q^{44} + 51030 q^{45} - 773024 q^{46} + 123114 q^{47} + 663552 q^{48} - 1718583 q^{49} + 2162800 q^{50} - 661716 q^{51} + 122816 q^{52} - 3004752 q^{53} - 472392 q^{54} + 4492720 q^{55} - 458240 q^{56} - 73062 q^{57} + 912896 q^{58} + 2852938 q^{59} + 120960 q^{60} - 665386 q^{61} + 3542320 q^{62} - 298161 q^{63} + 1572864 q^{64} - 5835930 q^{65} - 524448 q^{66} - 10545857 q^{67} - 1568512 q^{68} + 5217912 q^{69} - 6332240 q^{70} - 2039524 q^{71} - 1119744 q^{72} + 6858031 q^{73} - 1999896 q^{74} - 3649725 q^{75} - 173184 q^{76} + 6356164 q^{77} - 829008 q^{78} - 1723021 q^{79} + 286720 q^{80} - 1594323 q^{81} - 4887408 q^{82} + 5271608 q^{83} - 706752 q^{84} + 1474120 q^{85} - 4801944 q^{86} + 3081024 q^{87} - 1243136 q^{88} + 976224 q^{89} - 816480 q^{90} + 9819005 q^{91} + 12368384 q^{92} - 5977665 q^{93} + 984912 q^{94} - 11136310 q^{95} - 2654208 q^{96} - 16971584 q^{97} + 605952 q^{98} + 3540024 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 81 * q^3 - 192 * q^4 + 70 * q^5 + 1296 * q^6 - 895 * q^7 + 3072 * q^8 - 2187 * q^9 + 560 * q^10 - 2428 * q^11 - 5184 * q^12 - 3838 * q^13 - 3272 * q^14 - 3780 * q^15 - 12288 * q^16 - 24508 * q^17 - 17496 * q^18 + 1353 * q^19 - 8960 * q^20 + 35208 * q^21 + 38848 * q^22 - 96628 * q^23 - 41472 * q^24 - 135175 * q^25 + 15352 * q^26 + 118098 * q^27 + 83456 * q^28 - 228224 * q^29 + 15120 * q^30 - 221395 * q^31 - 98304 * q^32 - 65556 * q^33 + 392128 * q^34 - 136510 * q^35 + 279936 * q^36 - 249987 * q^37 + 10824 * q^38 + 51813 * q^39 + 35840 * q^40 + 1221852 * q^41 - 193320 * q^42 + 1200486 * q^43 - 155392 * q^44 + 51030 * q^45 - 773024 * q^46 + 123114 * q^47 + 663552 * q^48 - 1718583 * q^49 + 2162800 * q^50 - 661716 * q^51 + 122816 * q^52 - 3004752 * q^53 - 472392 * q^54 + 4492720 * q^55 - 458240 * q^56 - 73062 * q^57 + 912896 * q^58 + 2852938 * q^59 + 120960 * q^60 - 665386 * q^61 + 3542320 * q^62 - 298161 * q^63 + 1572864 * q^64 - 5835930 * q^65 - 524448 * q^66 - 10545857 * q^67 - 1568512 * q^68 + 5217912 * q^69 - 6332240 * q^70 - 2039524 * q^71 - 1119744 * q^72 + 6858031 * q^73 - 1999896 * q^74 - 3649725 * q^75 - 173184 * q^76 + 6356164 * q^77 - 829008 * q^78 - 1723021 * q^79 + 286720 * q^80 - 1594323 * q^81 - 4887408 * q^82 + 5271608 * q^83 - 706752 * q^84 + 1474120 * q^85 - 4801944 * q^86 + 3081024 * q^87 - 1243136 * q^88 + 976224 * q^89 - 816480 * q^90 + 9819005 * q^91 + 12368384 * q^92 - 5977665 * q^93 + 984912 * q^94 - 11136310 * q^95 - 2654208 * q^96 - 16971584 * q^97 + 605952 * q^98 + 3540024 * q^99

Introduction

L-functions

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